UTMA Functions and Graphing

Question 1

Which of the following represents the domain of f(x) = √(x − 3)?

Accepted Answer

x ≥ 3

Answer

The expression under a square root must be non-negative, so x − 3 ≥ 0, giving x ≥ 3.

Question 2

If f(x) = 2x + 1 and g(x) = x², what is (f ∘ g)(3)?

Accepted Answer

19

Answer

g(3) = 9, then f(9) = 2(9) + 1 = 19.

Question 3

The graph of y = f(x − 2) + 3 is a transformation of y = f(x). Which transformation is applied?

Accepted Answer

Shift right 2, up 3

Answer

Replacing x with (x − 2) shifts the graph 2 units right, and adding 3 outside shifts it 3 units up.

Question 4

Which function is an even function?

Accepted Answer

f(x) = x⁴ − 2x²

Answer

A function is even if f(−x) = f(x); for x⁴ − 2x², f(−x) = x⁴ − 2x² = f(x).

Question 5

What is the range of f(x) = −x² + 4?

Accepted Answer

(−∞, 4]

Answer

Since −x² ≤ 0, the maximum value is 4, and the parabola opens downward, so f(x) ≤ 4.

UTMA - University of Toronto Math Assessment Practice Test