PRE CALCULUS Functions 3

Question 1

What does the horizontal line test determine?

Accepted Answer

Whether a function is one-to-one

Answer

If every horizontal line intersects the graph at most once, the function is one-to-one and thus has an inverse.

Question 2

For f(x) = 3x + 6, what are the x- and y-intercepts?

Accepted Answer

x-intercept: (-2, 0); y-intercept: (0, 6)

Answer

Set f(x) = 0: 3x + 6 = 0 → x = -2; set x = 0: f(0) = 6.

Question 3

Which of the following represents an odd function?

Accepted Answer

f(x) = x³ - x

Answer

f(-x) = (-x)³ - (-x) = -x³ + x = -(x³ - x) = -f(x), confirming f(x) = x³ - x is odd.

Question 4

If f(x) = x² - 4 and g(x) = x + 2, what is (f/g)(x) in simplified form?

Accepted Answer

x - 2

Answer

f(x)/g(x) = (x² - 4)/(x + 2) = (x-2)(x+2)/(x+2) = x - 2, for x ≠ -2.

Question 5

What is the average rate of change of f(x) = x² on [2, 5]?

Accepted Answer

7

Answer

Average rate of change = (f(5) - f(2))/(5 - 2) = (25 - 4)/3 = 21/3 = 7.

PRE CALCULUS Practice Test