UTMA Functions and Graphing 2

Question 1

What are the x-intercepts of f(x) = x² − 5x + 6?

Accepted Answer

x = 2 and x = 3

Answer

Factoring gives (x − 2)(x − 3) = 0, so x = 2 and x = 3.

Question 2

Which of the following is a one-to-one function?

Accepted Answer

f(x) = 2x + 5

Answer

A linear function f(x) = 2x + 5 passes the horizontal line test, confirming it is one-to-one.

Question 3

What is the y-intercept of f(x) = (x + 3)(x − 1)?

Accepted Answer

−3

Answer

Setting x = 0 gives f(0) = (3)(−1) = −3.

Question 4

If f(x) = x² and g(x) = x + 1, what is (f + g)(2)?

Accepted Answer

7

Answer

(f + g)(2) = f(2) + g(2) = 4 + 3 = 7.

Question 5

The function f(x) = 1/(x − 4) has a vertical asymptote at:

Accepted Answer

x = 4

Answer

A vertical asymptote occurs where the denominator equals zero: x − 4 = 0 gives x = 4.

UTMA - University of Toronto Math Assessment Practice Test