Functions
Solving Functions
Transforming Functions
Writing Functions
Bonus
100
Which relations is a function?
Graph C, because it is the only one that passes the vertical line test.
100
Which function is an odd function?
F. f(x) = -x3 + 4 G. f(x) = 2x3 H. f(x) = x4 - 9 J. f(x) = x4 + 4x
G., because odd function is a function that is symmetric with respect to the origin.
100
Given f(x) = [[x - 1]], what is f(-4.5)?
-6, because this graph is a step function and the original step function the answer would be -5, but this function is shifted to the right/down 1 unit.
100
Francis orders a pizza. He uses a 20% off coupon and then pays $3 for delivery. Which composition function gives the total amount paid if x is the cost of the pizza, c(x) is the coupon function, and d(x) is the delivery function?
[d o c](x), c(x) = 0.8x
200
Given f(x) = x2 - 2x, find f(4).
f(4) = 8
200
Which function has a removable discontinuity?
A. f(x) = x/(x+3)
B. f(x) = (x^2-4)/(x+2)
C. f(x) = 1/(x+3)
D. f(x) = x^3-3
B., because f(-2) is undefined, where as the lim of f(x) as x approaches -2 is -4.
200
Which of the following results in the graph of f(x) = x2 being expanded vertically and reflected over the x-axis?
A. f(x) = 1/3x^2
B. f(x) = -3x^2
C. f(x) = -1/(x^2)+3
D. f(x) = -1/3x^2
G., because the coefficient in front of x is greater than 1, which means it will expand vertically; and the (-) out front reflects the function over the x-axis.
200
If f(x) = x2 + 1 and g(x) = 2x, find [f o g](x).
[f o g](x) = 4x2 + 1
300
Find the zero of
f(x) = -2/3x - 12.
x = -18 when f(x) = 0
300
What expression for A makes the limit of f(x) = A as x approaches infinity, correct, for
f(x) = 3/(x-4)
G., because as the denominator gets bigger and bigger, the function gets closer to 0.
300
Given the parent function p(x) = x3, what translation occurs in the graph of p(x) = (x - 7)3?
Moves 7 units to the right
300
Find the inverse of f(x) = 2x + 9.
f^-1(x) = (x-9)/2
400
What is f(-2) for f(x) ={|4x| if x < -2}
{x3 - 1 if x >= -2}
f(-2) = -9, because you have to use the bottom equation since it includes -2.
400
The function p(x) = -5x3 + 47x2 - 109x + 90 approximates the number of students on the debate team from 2004 to 2010 where x is the number of years since 2000. Which of the following best approximates the relative maximum of the function?
A. 5 B. 15 C. 97 D. 10,880
C., graph the function and find on the graph that the relative max is around 97.
400
Which of the following represents the graph of f(x) = |x3|?
Graph H., because x3 looks like graph F, but the absolute value takes everything in the negative y and puts it in the positive y.
400
Which function has an inverse that is also a function?
A. f(x) = |x|
B. f(x) = x^2
C. f(x) = (x+1)/x^2
D. f(x) = x^3
D., because the horizontal line test shows that there is only one x value for every y value.
500
Which relation is symmetric with respect to the x-axis?
A. xy = 2. B. x = y2 C. y = x2 D. y = 3
B., because it is a function of a porabola centered on the x-axis.
500
The height in feet of a rocket t seconds after launch is modeled by h(t) = -16t2 + 72t. Find its average speed from 3 to 4 seconds.
-40 ft/s
500
If f(x) = x - 3 and g(x) = 2x - 4, find (f + g)(x).
(f + g)(x) = 3x - 7
500
Henri buys a plant when it is 18 inches tall. It then grows 3 inches per year. What function can be used to find the number of years Henri had the plant given the height of the plant?
f(x) = (x-18)/3
500
If
f(x) = sqrt(x+2)
and (g o f)(x) = x - 1, find g(x).
g(x) = x2 - 3