Q: Which of the following describes the end behavior of $$f(x) = -2x^5$ + 3x^2$ - 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Q: Which of the following is a piecewise function?

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

Question 1

Which of the following relations is NOT a function?

Accepted Answer

A relation where the graph fails the vertical line test

Question 2

Given the function $$f(x) = |x|$$, which of the following describes its symmetry?

Accepted Answer

It is symmetric about the y-axis

Question 3

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

Accepted Answer

$$[3, \infty)$$

Question 4

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

Accepted Answer

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

Question 5

Which transformation will shift the graph of $$f(x) = x^2$ 4 units to the right and 3 units up?

Accepted Answer

$$f(x) = (x-4)^2$ + 3$$

Question 6

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

Accepted Answer

$$[0, \infty)$$

Question 7

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, which of the following is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 1$

Question 8

Which of the following functions is one-to-one?

Accepted Answer

$$f(x) = x^3$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

$$11 + 10i$$

Question 11

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

Accepted Answer

$$5 + 2i$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following describes the end behavior of $$f(x) = -2x^5$ + 3x^2$ - 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 14

A quadratic function $$f(x) = a(x-h)^2$ + k$$ has its vertex at:

Accepted Answer

$$(h, k)$$

Question 15

Which of the following is a piecewise function?

Accepted Answer

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

Question 16

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$\{x \mid x 
eq -2\}$$

Question 17

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

Accepted Answer

A function of the form $$f(x) = a_nx^n + a$$_{n-1}$$x^{n-1}$$ + \ldots + a_1x + $$a_0$$ where $$n$ is a non-negative integer and coefficients are real numbers

Question 18

A medical researcher models the spread of a virus using $$f(t) = 5t^2$ - 20t + 25. $$What is the minimum value of $$f(t)$$ and at what time $$t$$ does it occur?

Accepted Answer

Minimum at $$t = 2$$, $$f(2) = 5(2)^2$ - 20(2) + 25 = -15$$

Question 19

A chemical reaction is modeled by $$f(x) = x^3$ - 6x^2$ + 11x - 6. $$What are the zeros of $$f(x)$$?

Accepted Answer

$$x = 1, 2, 3$$

Precalculus Study Guide: Functions, Graphs, and Polynomial Concepts

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