$$f(x) = \begin{cases} x+2 & x \u003c 0 \\ x^2$ & x \geq 0 \end{cases}$$

Question 1

Which of the following relations is NOT a function?

Accepted Answer

A relation where $$f(x) = \pm \sqrt{x}$$ for $$x \geq 0$$

Question 2

Given the graph of $$f(x)$$, which test can be used to determine if $$f(x) is a $$function?

Accepted Answer

Vertical line test

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 4

What is the domain of $$f(x) = \sqrt{x-3} in $$interval notation?

Accepted Answer

$$[3, \infty)$$

Question 5

A function $$f(x) is $$said to be odd if:

Accepted Answer

$$f(-x) = -f(x)$$ for all $$x in $$the domain

Question 6

Which transformation describes the graph of $$g(x) = f(x-2) + 3$$ compared to $$f(x)$$?

Accepted Answer

Shift right 2 units and up 3 units

Question 7

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 8

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

Accepted Answer

$$2x^2 + 1$

Question 9

Which function is one-to-one?

Accepted Answer

$$f(x) = x^3$

Question 10

What is the inverse of $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{3}$$

Question 11

What is the product $$(2 + 3i)(4 - i)$$?

Accepted Answer

$$11 + 10i$$

Question 12

What is the complex conjugate of $$5 - 2i$$?

Accepted Answer

$$5 + 2i$$

Question 13

Solve $$x^2 + 4x + 8 = 0$ using the quadratic formula. What are the roots?

Accepted Answer

$$x = -2 \pm 2i$$

Question 14

What is the standard form of the quadratic function $$f(x) = 2(x - 3)^2$ + 5$$?

Accepted Answer

$$f(x) = 2x^2$ - 12x + 23$$

Question 15

A projectile is launched and its height is modeled by $$h(t) = -16t^2$ + 64t + 80. $$What is the maximum height reached?

Accepted Answer

$$h(2) = 144$$

Question 16

Which polynomial function has end behavior where $$f(x) 	o -\infty as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) = -x^3$ + 2x$$

Question 17

Find the zeros of $$f(x) = x^2$ - 5x + 6 by $$factoring.

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 18

Which of the following is a piecewise function?

Accepted Answer

$$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$

Question 19

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of $$\frac{f}{g}$$?

Accepted Answer

$$(-\infty, -1) \cup (-1, \infty)$$

Precalculus Study Guide: Functions, Graphs, and Polynomial Concepts

Study Guide - Practice Questions