TRIGAHHH
How do you define symmetry?
A perfect replica of a line or shape, only reversed.
What is the degree of this function: y = 3x^2 - 4x^5 + x - 1.
5
What is the line, or axis, of symmetry of the following equation? y= (x+2)^2 + 10
x=-2
If the binomial (x + y) is raised to the 6th power, what will just the variable portion of the expansion look like?
x^6 + x^5y + x^4y^2 + x^3y^3 + x^2y^4 + xy^5 + y^6
Expand: (x+1)^8
x^8 + 8x^7 + 28x^6 + 56x^5 + 70x^4+ 56x^3 + 28x^2 + 8x + 1
Consider: 3ab + 4b. Name the Terms.
3ab and 4b.
Which of the following is a point on the function y = 3x - 2?
(-2, -8)
If a certain function produces -36 as an answer for the x value of 5, which of the following intervals is most definitely negative?
(4, 10)
What is the leading coefficient of this function: y = x^3 - 2x^4 + 1
-2
Which of the following equals (x^2)/(x^3*x^n)?
1/(x^{n + 1})
What is the leading coefficient of this polynomial?
12
For the polynomial function f(x) = (x - 1)(x - 2)(x + 3), how many positive intervals are there?
2
How many intervals does the function f(x) = x have?
2
What does a^b equal if a = 4 and b = 3?
64
If there are 6 solutions, how many intervals are there?
7
Evaluate 8 choose 4, or...
70
Use Pascal's Triangle to determine the third term of the expansion of (4x+1)^4
96
What does 'Binomial Theorem' mean?
A mathematical formula used to expand two term expressions.
What is Pascal's Triangle?
A number pattern that identifies the coefficients for the expansion of polynomials.
A few interesting facts about Pascal's Triangle are:
All of these are correct.
Where do you look for the short run behavior?
Around the origin.
What does a negative leading coefficient do to a graph?
Flips it.
What is the short run behavior?
From the left approaching the origin, the graph goes to negative infinity. From the right approaching the origin, the graph goes to positive infinity.
What is the long run behavior of this graph?
It goes to y = 2.
What is the short run behavior of this graph?
It increases steadily.
How can you tell if a graph is from an Odd Degree Polynomial function?
The graph starts and ends on opposite sides of the x-axis.
Where do you look for the long run behavior?
To the far left and far right.
Expand (a + b)^5.
a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5
The outside edge of Pascal Triangle shows what number?
all 1's.
All polynomial graphs must:
be smooth and continuous.
Given f(x) = 6x; find f(5ab)
f(5ab) = 30ab
Which of the following polynomials has these intervals: (negative infinity, -6), (-6, 2), (2, 3), (3, positive infinity)?
f(x) = (x + 6)(x - 2)(x - 3)
All of the following are one-to-one functions, EXCEPT:
f(x) = 2
The graph for the equation x=10 is a _____
vertical line
Which equation is NOT equivalent to 2x + 4y = 6?
2x + 4y + 3 = 3
Which portion(s) of this piecewise function would include an open endpoint? f(x) = 2x +3, x>2 f(x) = 3x - 4, x = 2 f(x) = x-2, x <2
2x +3 and x-2
What is g(f(4)) if g(x) = x+1 and f(x) = √(x)?
3
Which of the following statements is true?
A function must always pass the vertical line test.
What is the domain of the function f(x) = x?
All numbers
If f(x) = x and g(x) = 1 / x, what is the domain of f(g(x))?
All numbers except 0
What is the domain of f(x) = 1 / x?
All numbers except 0
What is the range of the function f(x) = x^2?
All positive numbers and zero
The graph of y = x - 2 will pass through which quadrants?
I, III & IV
What are the horizontal asymptote(s) for the equation y = x^2 + 1?
None of these are correct
For a function f(x), what is f - 1 (3 * f(x))?
Not enough information
Test this equation for symmetry:
The equation has no symmetry.
Test the following equation for symmetry about the origin:
The equation is symmetrical about the origin.
Test this equation for symmetry:
The equation is symmetrical across the x-axis.
The symmetry of a graph is defined as _____.
an exact replica or reflection of a line
Find f(x) if f-1 (x) = x3 + 2
f(x) = (x - 2)(1/3)
The graph of y - x + 10 = - (8 + x) is a _____
horizontal line passing through the III and IV quadrants.
While reading your textbook, you find a function that has two inputs that produce the same answer. Based on this information, you know that this function is _____.
not a one-to-one function
The following function is _____. y=2x^3 - 6x
odd
Use factoring to find a solution of the following equation: 2x^2+8x = x^2+2x-8. (Remember that if one side of the equation equals zero, and the other side of the equation is a product, then at least one of the parts of the product must equal zero. For example, if 0 = x(3-x), then x must be 0 or (3-x) must be 0.)
x = -2
Solve for x and y. x + y = 5 x - y = -1
x = 2 and y = 3
Find x if 4x = 2^4.
x = 4
What are the restrictions of this function?
x > 8, x < 8
Which of the following is an implicit function?
x2-xy-y2=1
What is the line of symmetry for the following equation? y= 4x^2 + 16x -8
x=-2
What is the line, or axis, of symmetry of the following parabola?
x=-3
Manipulate the following equation to isolate the y variable. x - 3y = 12
y = -4 + x/3
Consider the slope of the lines given by the following functions. Which function has the steepest slope?
y = 2x+1
In the figure shown below, the graph of the yellow function is a translation of the graph of the blue function. If the expression for the blue function is y(x) = b(x), which of the following is the equation of the yellow function?
y(x) = b(x - 3) + 2
What are the horizontal asymptote(s) for the equation y = 1/(x^2-4)?
y=0
Which of the following is not a coefficient of this polynomial?
1
What is f(g(2)) if g(x) = x^2 and f(x) = x^3?
64
What is the most common piecewise function?
Absolute Value
Which kind of transformation would change the purple function below into the yellow one?
Reflection
What does 'Evaluating Polynomials in Function Notation' really mean?
Solve functions of many terms by writing the method in a specific mathematical way.
Test the following equation for symmetry about the origin: x + 3y = 27
The graph has no symmetry.
Test the following graph for symmetry about the origin:
The graph is not symmetrical about the origin.
Test the following points for symmetry: (3,4) (3,5) (3,6) (4,8) (3,-4) (3, -5) (3, -6) (4,-8)
The points are symmetrical across the x-axis.
Test the following points for symmetry: (2,3) (3,3) (3,4) (4,5) (-2,3) (-3,3) (-3,4) (-4,5)
The points are symmetrical across the y-axis.
Test the following points for symmetry about the origin: (-1,-5), (-3, -8) and (-5, -13); (1,5), (3,-8) and (5, -13)
The points have no symmetry.
The line of symmetry of a graph is defined as _____.
an imaginary line that runs through the center of a graph creating two perfectly identical halves
Solve the following equation for c. 2a - 3b + c - 3 = 6a + 4b - 12
c = 4a + 7b - 9
What is the domain of this function?
dom(f) = (-∞, 0) ∪ (0, ∞)
What is the domain of this function?
dom(f) = (-∞, 4) ∪ (4, ∞)
What is the domain of this function?
dom(f) = ℝ
The following function is _____. y= |x| + 4
even
This graph represents a(n) _____ function.
even
What is the inverse function of f(x) = x/8 + x + 2?
f -1 (x) = (8/9)(x - 2)
Which of the following is the inverse function of f(x) = 2x - 3?
f -1 (x) = (x + 3)/2
Which of the following is the inverse function of f(x) = 3x?
f -1 (x) = x/3
Write the composite function f(g(x)) when f(x) = x^2 + x + 1 and g(x) = x + 1.
f(g(x)) = (x + 1)^2 + (x + 1) + 1
Which piecewise function is represented by this graph?
f(x) = -3, x < 2 f(x) = 5 - x, x = 2 f(x) = -x + 7, x > 2
Which of the following is a one-to-one function?
f(x) = x + 9
All of the following are piecewise functions, EXCEPT:
f(x) = x² + 5x - 3 f(x) = x - 4
On the graph of a(n) _____ function, the left half of the graph exactly reflects the line or shape on the right half of the graph, except it is upside-down.
odd
For f(g(x)), the range for g(x) has to be within _____
the domain of f(x).
On the graph of an even function, _____.
the left half of the graph exactly reflects the line or shape on the right half of the graph
What is g(f(x)) if f(x) = g-1 (x)?
x
What are the vertical asymptotes for the equation y = 1/(x*(x-5))?
x = 0 and x = 5
What are the asymptotes for this equation?
x = 2 and x = -3
Solve for x and y. x - 3y = -1 2x - 2y = 2
x = 2 and y = 1
What is the line of symmetry for the following equation? y= -3x^2 + 15x -28
x=2.5
The implicit function x^2=y^2 is graphed below. Which functions give the same graph?
x=y x=-y
Which of the following is not a valid polynomial term?
x^-1
Expand f(x) = (x+3)^2.
x^2+6x+9
What is the leading term of this polynomial?
12x^7
Given f(x) = x^2 + 3x -2; find f(3).
16
How many functions y=f(x) are needed to represent the graph below?
2
If the following graph is an implicit function, then how many real functions would it take to graph it?
2
When the graph of f(x - 1) + 3 is changed into the graph of f(x + 1) + 3, the graph will shift in which direction?
2 units to the left
Find a * b if a = 2^6 and b = 2^8.
2^{14}
How many terms does this polynomial have?
4
Which of the following equations has a slope equal to -1/4?
(-4)y=x-8
If f(x) = x^2 and g(x) = x + 1, what is f(g(x))? Hint: For every x in f(x) put in g(x)
(x + 1)^2
Factor the quadratic x^2-4.
(x+2)(x-2)
Factor x^2+4x-5.
(x-1)(x+5)
What is the slope of the line given by the equation y + 3x = 2?
-3
How many times do the answers of a one-to-one function repeat?
0
What is the slope of the line tangent to the curve given by the equation y = (x-1)²+2 at the point (1,2)?
0
What is the range of f(g(x)) if f(x) = |x| and g(x) = cos(x)?
0 to 1
A one-to-one function crosses a horizontal line how many times?
1
What is the domain of a piecewise function?
Any input value where the function is defined
Which kind of transformation stretches or shrinks the graph of the function?
Dilation
How do you determine whether a function is an inverse of another function?
Find the composite of the functions
The graph of y = (1 + x)^2 will lie in which quadrants?
I & II
Which one of the following equals 2 * 2 * 2 * 2? I) 2^4 II) 2^2 * 2^2 III) 2^6/2^4
I and II
Which of the following are polynomials? I) f(x) = x^4+x II) f(x) = x^2+x*sin(x) III) f(x) = x+2*sin(2)
I only
Which of the following equations have a vertical asymptote at x = 1? I) y = 5/(x-5) II) y = 1/(x^2-1) III) y = 1/(x-1) * 1/(x-2)
II & III
Find the inverse function of f(x) = 1?
It does not have an inverse function.
What does 'Polynomial' mean?
Many numbers or terms.
