Question 1

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input has exactly one output.

Question 2

Given the function $$f(x) = x^2$ - 4x + 3$$, what is the value of $$f(2)$$?

Accepted Answer

$$-1$$

Question 3

Which graph represents the function $$f(x) = -x^2$?

Accepted Answer

A downward opening parabola centered at the origin.

Question 4

If $$f(x) = rac{1}{x}$$, which of the following describes the domain of $$f$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 0$$

Question 5

What is the range of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 6

Which of the following is the inverse of the function $$f(x) = 2x + 3$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-3}{2}$$

Question 7

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 8

Which of the following graphs represents an odd function?

Accepted Answer

A graph symmetric about the origin.

Question 9

Given $$f(x) = |x|$$, which of the following is true?

Accepted Answer

$$f(x) is an $$even function.

Question 10

Which of the following is the correct graph for $$f(x) = \sqrt{x-2}$$?

Accepted Answer

A curve starting at $$(2,0)$$ and increasing to the right.

Question 11

If $$f(x) = x^2$ and g(x) = 2x$, what is f(g(3$$))$$?

Accepted Answer

$$36$$

Question 12

Which of the following is the correct transformation for $$f(x) = x^2$ to f(x$$) = $$(x-3)^2 + 2$?

Accepted Answer

Shift right by 3 units and up by 2 units.

Question 13

Which of the following is the correct graph for $$f(x) = -|x|$$?

Accepted Answer

A 'V' shape opening downward with vertex at the origin.

Question 14

If $$f(x) = x^2$ - 4$$, what is the vertex of the parabola?

Accepted Answer

$$(0, -4)$$

Question 15

Which of the following is the correct domain for $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 2$$

Question 16

If $$f(x) = \sqrt{x}$$, what is $$f(9)$$?

Accepted Answer

$$3$$

Question 17

Which of the following is the correct graph for $$f(x) = x^3$?

Accepted Answer

An S-shaped curve passing through the origin.

Question 18

If $$f(x) = |x-2|$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$0$$

Question 19

Which of the following is the correct range for $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Precalculus Exam 1 Review: Graphs and Functions

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