Math
(3i + 4) + (4 + 3i) = ?
6i + 8
Functions of the form y = ax + b are called?
Linear Functions
Does the equation 1/4 cos2x = √2 have a solution?
No, because 4√2 > 1.
What is the range of f(x) = 1/x?
Range = all real numbers, y ≠ 0
True or False? 2^(2x) = 4x
TRUE
This state of affairs is indicated by the following notation: f: A→B, what is A called?
The Domain
This state of affairs is indicated by the following notation: f: A→B, what is B called?
The Range
Solve for x: 5(x + 3)2 = 125
x = 2, -8
Solve x^2 + 6 = 1
±i√5
What is the half-angle identity for tan(α/2)?
±sin α/(1 + cos α)
What is tan(30°)?
(1√3/)3
What is the highest power in the polynomial called?
Degree
True or False? α^logα^b = α
FALSE, α^logα^b = b
If two polynomials have the same terms, what does that mean?
They are equal.
3(x - 9) + 3 = 2x - 5
x = 19
Find arcsec(cos(171π)).
π
What is the radian measure of an angle a = 180°?
π
What is the radian measure of 15°?
π/12
What is the radian measure of an angle that is 1°?
π/180
What is the degree measure of an angle a = 1 that is in radians?
( π/180)°
What is the maximum of the quadratic function f(x) = 4(x + 5)^2 - 1?
(-5, 3)
What is the minimum of the quadratic function f(x) = x^2 - 2x - 3?
(1, -4)
What is the degree measure of 4.3 radians? Do not simplify.
(774/π )°
What is the sum identity for tan(α + β)?
(tan(α) + tan(β))/(1 - tan(α) + tan(β))
Find cos(15°).
(√2 + √3)/4
Find cos(2π/3 ).
- 1/2
Find sin(210°).
- 1/2
What is the x-intercept of the following equation: y = x + 2/3
- 2/3
Solve, 1/4 = 16x+3
- 7 /2
Find arccsc(sec( 3π/4 )).
- π/4, since sec( 3π/4 ) = -√2 so arccsc(-√2) = - π/4
Find sin( 5π/3 ).
- √3/2
What is i^2 equal to?
-1
What is sin(270°)?
-1
What is the domain of y = arccos(x)?
-1 ≤ x ≤ 1
(2 + 4i)^2= ?
-12 + 16i
Solve: |2x - 3| = 7.
-2 or 5
Add the following Polynomials: Q(x) = 7x4-3x3+ 2x2- 5x + 4 = 0 P(x) = -2x5-2x4+ 3x3- 4x2+ 10x + 6
-2x5+ 5x4+ 0x3- 2x2+ 5x + 10
What is arcsin(- 1/2)?
-30 degrees
(4 + 6i)(2 + 7i) = ?
-34 + 40i
x^2 - 3x - 9 < 0
-3√5 + 3 / 2 < x < 3√5 + 3 / 2
Ix| < 4
-4 < x < 4
What is arctan(-1)?
-45°
Find the remainder for (2x^6 - 3x^5 + 4x^3 - 6) ÷ (x + 1).
-5
What is the conjugate of (3 - 4i)^2?
-7 + 24i
To make y = tan(x) invertible what interval should we restrict its domain to?
-90° < x < 90°
Complete the following: tan(-α)
-tan(-α)
9 - x^2 ≥ -4x
-√13 + 2 ≤ x ≤ √13 + 2
Find the domain of f(x) = √x^2 + 1
-∞ < x < ∞
(i + 2) - (i + 2) = ?
0
Find cot( π/2 ).
0
Find tan(π).
0
What is cos(90°)?
0
What is cot(90°)?
0
What is sin(180°)?
0
What is tan(360°)?
0
tan α > 0 and cot α > 0 is true between what degree intervals?
0° < α < 90° or 180° < α < 270°
Which domain must we restrict y = cos(x) to make it one-to-one and invertible?
0° ≤ x ≤ 180°
(12i + 21)/(12i + 21) = ?
1
Find sec(4π).
1
Find sin(π/2)
1
What is cot(45°)?
1
What is sin(90°)?
1
What is tan(45°)?
1
e^(1n1) = ?
1
What is the conjugate of 1 + 2i?
1 - 2i
4^(-2) = ?
1/16
Find sin(π/6)
1/2
What is cos(60°)?
1/2
What is sin(30°)?
1/2
What is sin(arcsin(1/2))?
1/2
What is the product-to-sum identity for sin(α) cos(β)?
1/2 (sin(α + β) + sin(α - β)
What is the radian measure of an angle a and a length l of an arc intercepted by a?
1/r
(4 - 2i) + (7 - 2i) = ?
11 - 4i
y = 4x 9 + 12 What is the y-intercept?
12
Convert 2π/3 radians to a measure on degrees.
120°
(4 + i)(3 - 2i) = ?
14 - 5i
(4 - i)^2 = ?
15 - 8i
(4 - 2i)^3 = ?
16 - 88i
(7i + 9) /(4i + 12 =
17 /20 + 3 /10i
Solve: (13 + 7i) + (5 + 6i)
18 + 13i
The graph of y = tan x has asymptotes every ____ degrees.
180
Tangent has a period length of how many degrees?
180 degrees
What is the degree measure of an angle that is equal to π?
180 degrees
Find csc( 5π/6 ).
2
log4 16 (Round to 4 decimal places)
2
y = 3x + 2 what is the y-intercept?
2
y = 4x + 2 /3 What is the y-intercept?
2 /3
What is the sum-to-product identity for cos α + cos β?
2 cos(α+β/2 cos(α-β/2 )
Solve: 8 + 2(32- 42)/15 - 6(3 + 1)
2/3
What is the y-intercept of the following equation: y = x + 2/3
2/3
(4 - 2i)(7 - 2i) = ?
24 - 22i
(4i + 3)/(3i + 4) = ?
24/24 + 7i/25
Convert 3π/2 radians to a measure in degrees.
270°
A number subtracted by 9, equal 20, what is that number equal to?
29
2^4 ÷ 2^2 = ?
2^2 = 4
2^4 ∙ 2^2 = ?
2^6 = 64
(2^2 )^4 = ?
2^8 = 256
What is the double-angle identity for sin(2a)?
2sin α cos α
What is the radian measure of an angle that is 360°?
2π
9^(1/2) = ?
3
What is the x-intercept of the following equation: y = 2x + 3?
3
What is the y-intercept of the following equation: y = 2x + 3?
3
y = 3x + 2 What is the slope?
3
What is the conjugate of 3 - 21i?
3 + 21i
What is the conjugate of (2 - i)^2 ?
3 + 4i
What is arccos(√3/2 )?
30 degrees
What is arccot(√3)?
30 degrees
What is 11π/6 radians in degree measure?
330°
Sine has a period of how many degrees?
360 degrees
y = 4x + 2/ 3 What is the slope?
4
(4i + 3) (2i + 4) = ?
4 + 22i
y = 4x/ 9 + 12 What is the slope?
4/9
(6 + 2i)(6 - 2i) = ?
40
(7 - 2i)^2 = ?
45 - 28i
What is arctan(1)?
45 degrees
Convert 240° to a measure in radians.
4π/3
(21i + 12)/(12i + 21) = ?
56/65 + 33i/65
Convert 225° to a measure in radians.
5π/4
Convert 150° to a measure in radians.
5π/6
What is the amplitude of y = -6sin(5x + 34°)?
6
What is the degree measure of π/3 radians?
60°
Add the following polynomials: Q(x) = 6x5+4x3- 2x =0 P(x) = -2x2+ x - 6 = 0
6x5+ 4x3- 2x2- 2x - 6
Solve: (5 + 3i) + (2 - 5i).
7 - 2i
What is 42π radians equal to in degrees?
7560°
Convert 315° to a measure in radians.
7π/4
A number, times itself equals 64, what is that number equal to?
8 or -8
(7i + 9) (4i + 12) = ?
80 + 120i
Which basic property of mathematics is shown below? For any real number x there is a unique number, denoted by -x, such that x + (-x) = 0.
Additive Inverse
In the function y = Af(x) A is called the_________.,
Amplitude
What is the inverse of sine called?
Arcsin or sin-1
Which basic property of mathematics is shown below? For all real numbers x, y, and z, x + (y + z) = (x + y) + z
Associative Law of Addition
Which basic property of mathematics is shown below? For all real numbers x, y, and z, x ∙ (y ∙ z) = (x ∙ y) ∙ z
Associative Law of Multiplication
List three branches of science where trigonometry is applied and is an important tool.
Astronomy, geography, navigation
In general, rational functions can approach, without intersecting certain lines, what are these lines called?
Asymptotes
The expression a^n is called a power, what is a called?
Base
logac = logbc/logb a is known as the
Change of Base Formula
Fill in the blank: We say that a - bi is the ____ of a+ bi.
Conjugate
A function f is a ______ between two sets, A and B, that assigns to each element x in A one and only one element f(x) in B.
Correspondence
Which of the following trigonometric functions equals sin(90° - α) for 0° < α < 90°?
Cosine
What is the arcsin(4)?
Does not exist since there is no angle a for which sin α = 4
What is tan(90°)?
Does not exist, undefined
What is the domain of f(x) = 1/x?
Domain = all real numbers, x ≠ 0
The set of all possible inputs of a function is often referred to as?
Domain of the function
What is the domain and range of y = arcsin(x)?
Domain: -1 ≤ x ≤ 1, Range: -90° ≤ y ≤ 90°
What is the domain and range of y = arccos(x)?
Domain: -1 ≤ y ≤ 1, Range: 0° ≤ y ≤ 180°
What is the domain and range of y = cos(x)?
Domain: -∞ < x < ∞, Range: -1 ≤ y ≤ 1
What is the domain and range of y = arccot(x)?
Domain: -∞ < x < ∞, Range: 0° < y < 180°
What is the domain and range of y = arctan(x)?
Domain: -∞ < x < ∞, Range: 0° < y < 180°
What is the domain and range of y = sin(x)?
Domain: -∞ < y < ∞, Range: -1 ≤ y ≤ 1
What is the domain of the function h(x) = x^2?
Domain: all real numbers
What is the domain and range of y = sec(x)?
Domain: all real numbers EXCEPT where cos(x) = 0(90°k), Range: y ≥ 1 or y ≤ -1
What is the domain and range of y = csc(x)?
Domain: all real numbers EXCEPT where sin(x) = 0(180°k), Range: y ≥ 1 or y ≤ -1
What is the domain and range of y = tan(x)?
Domain: all real numbers except where cos(x) = 0, Range: All real numbers -∞ < y < ∞
What is the domain and range of y = cot(x)?
Domain: all real numbers except where sin(x) = 0, Range: All real numbers -∞ < y < ∞
What is the domain of the function f(x) = √x + 1?
Domain: all real numbers greater than or equal to 0
If A > 1, then we get the graph of y = Af(x) by _____the graph of y = f(x) along the y-axis by a factor of A.
Expanding
If A > 1 what does this do to the graph of y = Af(x)?
Expands the graph
The expression a^n is called a power, what is n called?
Exponent
True or False? log(bd) = log(b) - log(d)
FALSE
True or False? sin(-α) = sin(α)
FALSE
True or False? α^m + α^n = α^(m+n)
FALSE
True or False? √3x = 5 is a rational equation.
FALSE
True or False? √x + 2 = 0 is a rational equation.
FALSE
True or False? The inverse of sine is defined over the domain of all real numbers.
FALSE
True or False? tan(2α) = (2 tan(α))/(1 + tan2 α)
FALSE, (2 tan(α))/(1 - tan2 α)
True or False? (ab)^n = a^n + b^n
FALSE, (ab)n = a^nb^n
True or False? 1 + cot^2 α = 1 /sin α
FALSE, 1 + cot2 α = 1 sin2 α
True or False? For any three real numbers x, y, and z, if x < y then x + z < y - z
FALSE, For any three real numbers x, y, and z, if x < y then x + z < y + z
True or False? For any three real numbers x, y, and z, if x < y, y < z, then x > z.
FALSE, For any three real numbers x, y, and z, if x < y, y < z, then x < z
True or False? A/sin a = B/sin a= C/sin a
FALSE, a/sin a = B/sin β = C/sin y
True or False? a^2 = b^2 - 2b cos(a)
FALSE, a^2 = b^2 + c^2 - 2bc cos(a), by Law of Cosines
True or False? For any |a| ≤ 1 arccos(-a) = 360° - arccos(a)
FALSE, arccos(-a) = 180° - arccos(a)
True or False? l is negative if a is a positive angle.
FALSE, l is negative if a is a negative angle.
True or False? logab d = logαb ∙ logα d
FALSE, logab d = logαb + logα d
True or False? 1 /sin α is denoted by sec α
FALSE, sec α is denoted by 1/ cos α
True or False? sin α - sin β = 2 cos(α-β/2 sin(α-β/2 )
FALSE, sin α - sin β = 2 cos(α+β/2 sin(α-β/2 )
True or False? cot α = sin α /cos α
FALSE, tan α = cot α = sin α /cos α
True or False? α^0 = 0
FALSE, α^0 = 1
True or False? The Rational Root Theorem states that: let P(x) and K(x) be two polynomials, where K(x) is not the zero polynomial. Then, there exist two unique polynomials Q(x) and R(x) such that P(x) = K(x)Q(x) + R(x); the polynomial Q(x) is the quotient, and the remainder R(x) is either the zero polynomial or of a degree that is less than the degree of K(x).
FALSE: The Division Algorithm
What term do we use to indicate dependencies between quantities?
Functions
A number that can be admitted into a function is called?
Input
If there exists a function g such that y = f(x) if and only if x = g(y), then we say that f is _______ and g is the _____ of f.
Invertible, inverse
Which theorem states a/sin a = 2r?
Law of Sines
State the Law of Sines.
Let ABC be any triangle with a, b, c and angles a, β, and y. Let r be the radius of the circle circumscribing the triangle. Then a/sin a = b/sin β = c/sin y = 2r
What is the Law of Cosines?
Let ABC be any triangle with a, b, c and angles a, β, and y. Then a^2 = b^2 + c^2 - 2bc cos(a), b^2 = a^2 + c^2 - 2ac cos(β), c^2 = b^2 + a^2 - 2ab cos(y)
The function y = loga x is called the ________
Logarithmic equation
What is it called when a function can have more than one input corresponding to one output?
Many to one function
For any real number x different from 0, there is a unique number, denoted by x -1, such that x ∙ x -1 = 1.
Multiplicative Inverse.
Logarithms with base e are called _________.
Natural Logarithms
Is √3 a rational number?
No, it is irrational
Is tangent a one-to-one function?
No, it is not because there are infinitely many values of x such that tan(x) = y
What is arctan(tan90°)?
Not defined because tan90°is not defined.
An input's corresponding number under the function is called a(n)?
Output
Consider a function f(x) = f(x + T). What is T called?
Period
What are equations like the following called? 2x3+ 4x2- x + 9 = 0 and -3x4+ 5x3- 2x + 12 = 0
Polynomial equations
The expression a^n is called a______
Power
In which quadrant or quarter does 2/π radians belong in?
Quadrant I, 2/π = 36.5°
In which quadrant or quarter does 3π/4 radians belong in?
Quadrant II
In which quadrant does 14π/12 belong in?
Quadrant III
In which quadrant does 11/3 belong in?
Quadrant IV
Functions of the form y = ax2 + bx + c, where a ≠ 0, are called?
Quadratic functions
There are two ways to measure angles in trigonometry, what are they?
Radians and degrees
What is the correct mathematical term for the measurement from the center point of a circle to its edge?
Radius
The set of all the outputs of a function is referred to as?
Range of the function
What are the range of the function h(x) = x^2?
Range: all non-negative real numbers
What are the range of the function f(x) = √x + 1?
Range: all real numbers greater than or equal to 1
What is an equation that involves only polynomials or rational expressions?
Rational equation
If 0 < A <1, then we get the graph of y = Af(x) by _______ the graph of y = f(x) along the y-axis by a factor of A.
Shrinking
If 0 < A < 1 in y = Af(x) what does this do to the graph?
Shrinks the graph
What does the imaginary number i represent?
Square root of -1
What do you call a function when any line parallel to the x-axis that intersects the graph will intersect it in two points that are equidistant from the y-axis?
Symmetric
How do you find the period of a function y = f(ax)?
T1=Ta
True or False? (a/b)^n = a^n/b^n
TRUE
True or False? (an)^m = a^(n∙m)
TRUE
True or False? 1/x + 2 = 0 is a rational equation.
TRUE
True or False? 3x + 7 - x^2 = 0 is a rational equation.
TRUE
True or False? 3x(x - 4)^2 = 0 is a polynomial equation.
TRUE
True or False? An invertible function f can have only one inverse function.
TRUE
True or False? For 0° < α <90°, sin α > 0 and cos α < 0
TRUE
True or False? For 90° < α < 180°, sin α > 0 and cos α < 0
TRUE
True or False? If the radian measure of an angle a is s, then the degree measure of a is ( π/180 ∙ s)°.
TRUE
True or False? Since y = loga x admits only positive inputs, its graph is located in the half plane to the right of the y-axis.
TRUE
True or False? The Factor Theorem states that: the polynomial x - a is a factor of P(x) if and only if P(a) = 0.
TRUE
True or False? The graph of f -1(x) = (x + 8)/2 is the reflection of f in the line y = x.
TRUE
True or False? The radian measure 1/r is independent of the choice of the radius r.
TRUE
True or False? The x-intercept of the log function is 1, because logax = 0
TRUE
True or False? a, the base of the logarithm, must be different from 1
TRUE
True or False? cos(360°) = 1
TRUE
True or False? cos(α + β) = cos(α) cos(β) - sin(α) sin(β)
TRUE
True or False? cos(α) cos(β) = 1/2 (cos(α + β) ± cos(α - β))
TRUE
True or False? i^3= -i
TRUE
True or False? l is positive if a is a positive angle.
TRUE
True or False? loga c = logb c logb a
TRUE
True or False? loga1 = 0
TRUE
True or False? logab^q = q logαb
TRUE
True or False? logaα = 1
TRUE
True or False? sin(α/2) = ± √1 - cos(α)/2
TRUE
True or False? sin^2 α + cos^2 α = 1
TRUE
True or False? α^m ∙ α^n = α^(m+n)
TRUE
True or False? α^m/α^n = α^(m-n)
TRUE
True or False? √x^2 = 4 is a rational equation.
TRUE
True or False? 2^6 = 2 ∙ 2^5
TRUE
True or False? For any three real numbers x, y, and z, if x < y and z < 0, then zx > zy
TRUE
True or False? For any three real numbers x, y, and z, if x < y and z > 0, then zx < zy
TRUE
True or False? For any two real numbers x and y, one and only one of the following is true: x < y, x = y, or x > y
TRUE
True or False? For any |a| ≤ 1 arcsin(-a) = -arcsin(a)
TRUE
True or False? The cotangent function is only invertible from 0° < x < 180°
TRUE
True or False? The equations 2x - 9 = 34 and 2x - 43 = 0 are equivalent.
TRUE
True or False? cosA = b /c sinA
TRUE
True or False? sin(180°k - a) = sin(α) for any integer k
TRUE
True or False? tan α ∙ cot α = 1
TRUE
True or False? tan(α + 180°k) = tan(α)
TRUE
True or False? tan^2 α + 1 = sec^2 α
TRUE
y = logax is increasing when a >1 and decreasing when 0 < a < 1.
TRUE
What Theorem is the following? Let P(x) = an xn + an-1xn-1 + ... a1 x + a0 be a polynomial with integer coefficients. If a reduced fraction m k is a solution to the equation P(x) = 0, then m divides a0 and k divides an
The Rational Root Theorem
In y = logax, what is a called?
The base of the log
Tom took a number, multiplied it by 3 and subtracted it by 8 and got 85. What is Tom's initial number?
The number is 31.
A number multiplied by itself, plus 16 is equal to 80. What is the number?
The number is 8 or -8.
Along which axis does the amplitude of a function expand or shrink the graph?
The y-axis
What does the term "trigonometry" mean?
Triangle measurement
What is tan(270°)?
Undefined or does not exist
Find csc(44π).
Undefined, any multiple of 2π means sine equals 0 and csc = 1/sin
Find tan( 3π/2 ).
Undefined, does not exist
When does the discriminant tell us we have no real solutions?
When b2- 4ac < 0
When does a quadratic equation have no real solutions?
When its solutions are not real numbers, or when the discriminant is less than zero.
Are the following two equations equivalent? 4x - 16 = 4 and 4x - 20 = 0
Yes
Which basic property of mathematics is shown below? For all real numbers x and y, x ∙ y = 0 if and only if x = 0 or y = 0 or both x and y are equal to 0.
Zero Factor Property
What is the name of the polynomial when all the coefficients are zeros?
Zero Polynomial
What is the conjugate of a - bi?
a + bi
a^(1/n) = n^√a if and only if?
a > 0 and n a natural number
What are the coefficients of the following equation? 5x5- 3x4+ 75x3+ 9x2- 5x + 1
a5= 5, a4= -3, a2= 9, a1= -5, a = 1
List one of the properties of the Law of Cosines.
a^2 = b^2 + c^2 - 2bc cos(a), b^2 = a^2 + c^2 - 2ac cos(β), c^2 = b^2 + a^2 - 2ab cos(y)
Find arctan(csc(π/4)).
arctan(√2)
What does the discriminant look like?
b2- 4ac
For 270° < α < 360°, what is the sign for cos α?
cos α > 0, positive sign
Complete the following identity: cos(-α) =
cos(α)
What is the double-angle identity for cos(2a)?
cos2 α - sin2 α θ
What is another form of writing arccot(x)?
cot -1(x)
What is the number e equal to? (Round to 5 decimal places)
e = 2.71828
Find the inverse of f(x) = 1/x + 1
f -1(x) = 1/x- 1
Find the inverse of f(x) = x^5+ 1.
f -1(x) = 5^√x - 1
Find the inverse of f(x) = 2x + 3/x + 1
f ^-1(x) = 3 - x/x - 2
What is the composition of g(x)= x + 4, h(x) = x^2?
f(x) = (x + 4)^2
What is the composition of g(x) = x/3, h(x) = x^2?
f(x) = (x/3)^2
What is the composition of g(x) = x - 5, h(x) = 3^x?
f(x) = 3^(x-5)
Find the range of f(x) = x + √x
f(x) ≥ 0
Find the inverse of the function f(x) = e^(-4x) + 2
f^-1(x) = [-1n(x - 2)]/4
Find the inverse of the function f(x) = 1/21n3x.
f^-1(x) = e^(2x)/3
Find the inverse of f(x) = 2x - 8
f^-1(x) = x + 8/2
When the leading coefficient of a quadratic equation is positive, the function will have a _______.
minimum
Expressions of the form xk, where k is a non-negative integer are called
monomials
What is the sign for sin α between 180° < α < 270°?
sin α < 0, negative sign
For 90° < α < 180°, what sign does sine exhibit?
sin α > 0, positive sign
sin(α) cos(β) - cos(α) sin(β) is the difference identity for which trigonometric function?
sin(α - β)
The sum identity for sin(α + β) =
sin(α) cos(β) + cos(α) sin β
1/2 (cos(α - β) - cos(α + β) is the product-to-sum identity for which product of trigonometric functions?
sin(α) sin(β)
What is the correct identity for cot(α) ± cot(β)?
sin(β ± α)/sin(α)sin(β)
What are the six trigonometric functions?
sine, cosine, tangent, cotangent, sec, and csc
For 270° < α < 360°, what are the signs for tangent and cotangent?
tan α < 0 and cot α < 0, negative signs
How is cotangent of a defined using knowing the tangent of α, for 0° < α < 90°?
tan(90° - α)
-3x + 15 > 60
x < -15
Find the domain of y = 2/(x^2 - 4)
x < -2 or -2 < x < 2 or x > 2
-3x > 20
x < -20/3
Find the domain of f(x) = x + 1 x
x < 0 or x > 0
-3x + 24 > 0
x < 8
Solve for x: -7x2 + x + 9 = -6x
x = −7±�301 -14
What is the solution to a quadratic equation when the discriminant Δ = 0?
x = - b/2a
Solve for x: x3 + 2021x + 2022 = 0.
x = -1
Solve for x: x2 + 2x - 10 = 0.
x = -1 + √11 or x = -1 - √11
Solve for x: x3 + 2x2 - x - 2 = 0.
x = -1 or x = 1 or x = -2
Solve for x: 27x3 + 18x2 - 3x - 2 = 0.
x = -1/3 or x =1-3 or x = -2/3
57(x + 8) = 3
x = -151/19
Solve for x.-2x2- 5x = 2
x = -2, x = -0.5
Solve for x: -√2x2+ √3x = -13
x = -2.4807, x =3.7055
Solve for x: -10x^2- 34x - 12 = 0
x = -2/5 , x - 3
Solve for x: (x + 3)(x - 2)(x + 9)(x - 3) = 0.
x = -3, 2, -9, 3
Solve sin(-2x) = 1
x = -45° - 180°k
What is the axis of symmetry for f(x) = 4(x + 5)^2 - 1
x = -5
Solve the equation: sin(x - 30°) = 1/√2
x = -75° + 360°k, x = 165° + 360°k
Solve for x: 4^(x+2) = 16
x = 0
Solve: (x + 4)^2
x = 0, x = -8
Find the value of x by solving the below equation 8x + 2 = 10
x = 1
Solve for x: 3^(2x) = 9
x = 1
Solve for x: x - 4 /x^2 - 3x - 4 = 1/ 2
x = 1
What is the axis of symmetry for f(x) = x^2 - 2x - 3
x = 1
Find the real solutions of x: (x2 + 2x + 1)^2 = 16.
x = 1 or x = -3
Solve for x: -x^2+ 6x - 6 = 0
x = 1.2679, x = 4.7321
logx (100) = 2
x = 10
Solve cot(3x) = 1
x = 15° + 60°k
Solve for x:(3x - 2)(x - 3) = 40
x = 17/3 or x = -2
-2.3x + 4.6 = 0
x = 2
Solve for x: 2^(2x+1) = 32
x = 2
√x + 5 = 5
x = 20
log5 x = 2
x = 25
Solve for x: 6x/ (x - 9) = 9
x = 27
Solve for x: (-2)^x = -8
x = 3
Solve for x: (3x - 2)/(x - 4) = (x + 4)/(x - 4)
x = 3
Solve for x: 1/2(6x - 8) + 3(x + 2) = 4(2x - 1)
x = 3
Solve for x: 2^(2x+1) = 128
x = 3
Solve for x: x^2 - 3x + 4 = 0
x = 3 /2 + √7i /2 , x = 3 /2 - √7i /2
log3 x + log3 (x + 6) = 8
x = 3(√730 - 1)
x^2 - 9 = 0
x = 3, -3
Solve tan(2x) = √3
x = 30° + 90°k
Solve for x: x^2 + 9 = 0
x = 3i, -3i
Solve for x: x^2 - 16 = 0
x = 4, -4
Solve for x: x^2 - 3x - 4 = 0
x = 4, x = -1
Solve for x: x^2 - 16 = 0
x = 4i, -4i
Solve for x: -3x + 5 = 0
x = 5/3
x^2 - 12x + 14 = 0
x = 6 + √22, x = 6 -√22
log4 x = 3
x = 64
Solve for x: -0.1x^2+ 1.1x - 2.8 = 0
x = 7, x = 4
Find the value of x by solving the below equation 7x + 6 = 62
x = 8
Solve: √x + 1 = 9
x = 80
9x/19 = 91/19
x = 91/9
Solve for x: 4 61 (x + 8) = 7
x = 98.75
Solve for x: x^2 - 36 = 0
x = ±6
√x^2 + 1 = 9
x = ±√80
What is the formula for the quadratic equation?
x = −b±�b2 − 4ac 2a
√3 - x^2 = 1
x = √2, x = -√2
Solve for x: (3x - 2)/(x - 4) = -(x + 4)/(x - 4)
x =-1/2
Solve for x: - 3/2x^2+ 1/2x + 1 = 0
x =-2/3 , x = 1
3 / x + 1 > 0
x > -1
3x - 5 > 8
x > 13/3
4x - 8 > 19
x > 27/4
2 + 2x ≤ x^2
x ≤ -√3 + 1 or x ≥ √3 + 1
Find the domain of f(x) = x + √x
x ≥ 0
|x| ≥ 8
x ≥ 8 or x ≤ -8
Multiply: P(x) = x^3- x^2+ x Q(x) = x^7+ x^5+ x^3
x^10 - x^9+ 2x^8- x^7+ 2x^6- x^5 + x^4
What is the point-slope form equation?
y - y1 = m(x - x1)
Find the inverse of the following equation: y = x^2 - 3x + 6
y = 3 - �4x − 15/2 , 3 + �4x − 15/2
What is the composition g(x) = 3x, h(x) = 4^x?
y = 4^(3x)
What is the general structure of quadratic equations?
y = ax^2+ bx + c
Find the inverse of the following equation: y = x - 5
y = x + 5
The coefficients a and b determine the form of the graph for y = ax + b, for (0, b) is where the function intersects the _______.
y-axis
For y = ax + b, what is b called?
y-intercept
How do you find the radian measure of an angle a = n°?
π/180 ∙ n
What is the radian measure of 90°?
π/2
Find arcsin(cos(π/6)).
π/3
Find arccot(cos(10π)).
π/4
What is the radian measure of 45°?
π/4
Find arccos(sin( 2π/3 )).
π/6
What is the radian measure of 30°?
π/6
Find cos(π/4).
√2/2
What is cos(45°)?
√2/2
What is sin(45°)?
√2/2
What is cot(30°)?
√3
What is tan(60°)?
√3
What is cos(30°)?
√3/2
What is sin(60°)?
√3/2
Find tan( 7π/6 ).
√3/3
What is cot(60°)?
√3/3
