MTH 111 FINAL

Q: Find the vertex of the parabola y = 3(x_2)^2+1

(-2,1)

Q: Solve the rational inequality x-1/x+3 <= 0

(-3,1]

EXAM II BEGINS (as of now assume you do not know how to do any of them, go back and put stars where needed!!!) : Q: Solve the quadratic inequality 4x^2 + 4x - 3 > 0

(-inf, - 3/2) u (1/2, inf)

M: identify the interval on the x-axis where f(x)=3(x+2)^2-5 is decreasing/ increasing

(-inf, -2) (-2, inf)

Q: Solve the inequality x(x+2)(x-3) < 0

(-inf, -2) u (0,3)

*Q: Let f(x0 = 3x-5 and g(x) = 2x +3. What is the domain of the quotion function f/g?

(-inf, -3/2) u (-3/2, inf)

Q: solve the inequality: |5-2x| > 3

(-inf, 1) u (4, inf)

Q: Solve the inequality |2x-1| <= - 3

(-inf, 1]

Q: 3 -2x >= 15

(-inf,-6]

Q: Find the vertex of the parabola y=4x^2-16x+1

(2,-15)

Q: Find the x-intercept of the line with equation 2x - 5y = 7

(7/2, 0)

M: Equation to find vertex if equation is in form y = a(x-h)^2-k

(h,k)

Q: Factor x^3 - 3x^2 + x - 3

(x^2+1)(x-3)

Q: Factor x^5 - 4x^4 - 4x + 16

(x^4-4)(x-4)

M: Perpendicular slope of 2?

-1/2

Q: What is the value of csc (11pi/6)

-2

Q: Let f(x0 = {(-3, -11), (2,-3),(1,2)} and g(x0 = 2x^2-4. Find f(x) + g(-1)

-5

Q: Find an angle that is not coterminal with pi/2

-5pi/2

Q: Find the equation of the line that passes through the points (5,3) (2,-4) - put into form ax + by = c

-7x + 3y = -6

Q: Rationalize 3-i/-2+3i and write the complex number in the form a + bi, where a and b are real numbers

-9/13-7/13i

M: Equation to find the zeroes of a function

-b +- sqrt b^2 - 4ac / 2a

*Q: What is the value of cot(sin^-1(-1/2)

-sqrt 3

Q: Find cot (5pi/6)

-sqrt 3

Q: What is the value of cos(5pi/4)

-sqrt2/2

*Q: Find the equation of a line passing through (-6,1) and perpendicular to the ling 2x + y = 5

...

*Q: Which of the following is a vertical asymptote of y = tan (x)?

0

*Q: Using identities, fully simplify sin^2x(1+cot^2x)

1

Q: What is the value of sin(390degrees)?

1/2

*Q: A guy wire of length 100 ft runs from the top of an antenna to the ground. If the angle of elevation of the top of the antenna, sighting along the guy wire, is 50 degrees, exactly how tall is the antenna?

100 * sin(50degrees) ft.

Q: Find the distance between the points (-4,1) and (1,13)

13

Q: Assume that theta is an angle in standard position whose terminal side contains the point (-sqrt 3, 1). Find the exact value of csc(theta)

2

Q: Given theta is in Quadrant II and cos (theta) is -4/5, find sin (theta)

3/5

Q: Let f(x) = 3x - 6 and g (x) = x^2 + 2x - 1. Compute f(x) * g(x)

3x^3 - 15x + 6

Q: Determine the period of y = tan(pi/4x)

4

Q: Compute (7+3i)^2 and write your answer in the form a + bi where a and b are real numbers

40 + 42i

Q: Find (fog) (x) if f9x) = x^2 + 2 and g(x) = 2x = 3

4x^2 + 12x + 11

Q: Compute (6+4i)(6-4i)

52

Q: Find f(-1) + f(0) if f(x) = {x^2 + 1 for x <= -1 {2x+5 for x > -1

7

Q: Convert 315 degrees to radians

7pi/4

*Q: What is the remainder when p(x) = x^4+x^3-x^2-2 is divided by x-3?

97

M: How to tell if a function is 1:1?

If a function has no two ordered pairs with different 1st coordinates and the same second coordinate

Q: Name the quadrant in which the angle -5pi/6 is located

Quadrant III

Which one have the period pi/|b| instead of 2pi/|b|

Tan and cot

M: When they ask the "which of the following is not 1:1"` question, what answer will it be?

The one that is an absolute value

M: On the test, when it asks which one is not an identity, what is probably the answer?

The only one besides the ones you have memorized that does not have a 1 in it

Q: Find the zeroes of the function f(x) = x^3 - x^2 - 12x

X = 0, X = 4, X = -3

Q: Simplify x+1 / x^2-3x-4 * x^2-16/x-8

X+4 / x-8

Q: Find the polynomial of degree 3 with real coefficients that has the factors (x+2i) and (x-3)

X^3-3X^2+4X-12

* Q: Determine the range of f(x) = {x+1 for x >= 0 {-x+2 for x<0

[1,inf)

Q: Find the domain of the function g(x) = sqrt x -3

[3, inf)

M: Equation to show translation of a graph?

a(x-h)^2 + k

M: Equation to find vertex *

a(x-h)^2+k

Q: Determine the amplitude, period, and phase shift of y = 3sin(x-pi)+1

amp = 3, per = 2pi, phase shift = pi

Q: Determine the amplitude, period, and phase shift of y = -4sin(2x)+1

amp = 4, per = pi, phase shift = 0

M: The problem about the f(a+h) crap, what will the answer not include?

any 4's, and 'ah's"

M: Equation to find amplitude, phase shift, period

asin(bx-c)+d

M: Phase shift equation

c/b

M: What do all the even identity functions look like? (use cos as an example)

cos(-x) = cos(x)

*Q: f(x) = (x-2)^2(x+1). Where does it cross the y-axis, where does it cross/touch at the x-axis, where does it cross/touch at the x-axis?

crosses the y-axis at y=4, touches x-axis at x=2, crosses x-axis at x=-1

M: What is the distance formula? **

d = sqrt (x2 - x1) ^2 + (y2 - y1) ^2

Q: Given f(x) = 3x - 2 /5, find the inverse f^-1 (x)

f(x) = 1/5(3y-2)

M: what are the odd identity functions?

f(x) = csc(x), f(x) = sin(x), f(x) = tan(x), f(x) = cot(x)

M: What are the even identity functions?

f(x) = sec(x), f(x) = cos(x)

Q: Let f(x) = |x| + 1 AND G(X0 = 2X^3 + X^2 odd, even, or neither?

f(x) = |x| + 1 is even, g(x0 = 2x^3 + x^2 is odd

M: "h" translates graph?

h units left

M: "-h" translates graph?

h units right

* Q: If f(x) = x^2 + 2x, then find f(a + h ) - f (a)

h^2 + 2a = 2h

M: How to tell if a function is odd or even:

if f(-x) = f(x) it is even. if f(-x) = -f(x) it is odd.

M: "-k" translates graph?

k units down

M: "k" translates graph?

k units up

M: Equation to find slope:

m = y2 - y1 / x2 - x1

Which of the following polynomials has the root -2 with multiplicity 1 and 3 with multiplicity 2?

p(x) = x^3 - 4x^2 - 3x + 18

Q: What is the polynomial that has the root 2 with multiplicity 2 and -3 with multiplicity 1?

p(x) = x^3 - x^2 - 8x + 12

*Q: What is the value of sec^-1(2)

pi/3

M: Trig ratios: Equation to find r ?

r = sqrt x^2 + y^2

M: What do all the odd identity functions look like? (use sin as an example)

sin(-x) = -sin(x)

M: What are the three pythagorean identities?!

sin^2 alpha + cos^2 alpha = 1, 1 + cot^2alpha = csc^2alpha, tan^2alpha+1 = sec^2alpha

Q: What is the value of cos(-pi/4)

sqrt 2 / 2

Q: What is the value of tan(pi/3)?

sqrt 3

Q* What is the value of tan(30degrees)?

sqrt 3 / 3

Q: What is the value of sin(-240degrees)?

sqrt 3/2

Q: Find the zeroes of the function f(x) = (x-2)(x^2-5)

sqrt 5, - sqrt 5, 2

Q: Find the zeroes of the function f(x) = x^3 - 3x^2 - 7x + 21

sqrt 7, -sqrt 7, 3

*Q: How to tell if an equation defines y as a function of x?

use inverse , if you get something like y^2 it doesnt

Q: solve for x: 9x + 2(-3x -4) = -14 - 9x

x = - 1/2

Q: Find the vertical asymptote(s) of the function f(x) = x(x+2) / x^2+3x+2

x = -1

*Q: Find the equation of the line perpendicular to the line y=7 that passes through the point (-3,4)

x = -3

Q: Find the zeroes of the function f(x) = x^2 - 2x + 2

x = 1 + i, x = 1 - i

M: Trig ration for cos

x/r

Q: Find a polynomial with real coefficients that has -2 and 3i as roots

x^3+2x^2+9x+18

****M: Equation of point slope form:

y - y1 = m(x - x1)

*Q: Determine the end behavior of the f(x) = (x-5)^3(x-2)^2(x-1)^1 (y is going where as x is going where and y is going where as x is going where)

y -> inf as x -> -inf and y -> inf as x -> inf

Q: Find the horizontal asymptote(s) of the function f(x) = 4x^2-2/-2x^2+9x-7

y = -2

Q: Given f(x) = x^3 + 3, Find the inverse f^-1 (x)

y = ^3 sqrt x - 3

M: Trig ration for sin

y/r

M: Trig ration for tan *

y/x

M: Equation for axis of symmetry

y=-b/2a

*Q: Find all (including multiplicity) real and imaginary roots of the following equation 3x^5 + 27x^3 = 0

{0,0,0, 3i, -3i)