UTMA Functions and Graphing 3

Question 1

What is the inverse of g(x) = (x/2) − 4?

Accepted Answer

g⁻¹(x) = 2x + 8

Answer

Set y = x/2 − 4, swap to get x = y/2 − 4, then solve: y = 2x + 8.

Question 2

The function f(x) = 3x² − 12x + 1 has its vertex at x = ?

Accepted Answer

x = 2

Answer

The vertex x-coordinate is −b/(2a) = −(−12)/(2·3) = 12/6 = 2.

Question 3

Which of the following graphs has a horizontal asymptote at y = 0?

Accepted Answer

f(x) = 2/(x + 1)

Answer

For rational functions where the degree of the denominator exceeds the numerator, the horizontal asymptote is y = 0.

Question 4

If f(2) = 5 and f is a linear function with slope 3, what is f(0)?

Accepted Answer

−1

Answer

Using point-slope: f(x) = 3x + b; plugging in f(2) = 5 gives b = −1, so f(0) = −1.

Question 5

What is the period of the function f(x) = sin(2x)?

Accepted Answer

π

Answer

The period of sin(bx) is 2π/b; with b = 2, the period is 2π/2 = π.

UTMA - University of Toronto Math Assessment Practice Test