Question 1

Which of the following relations represents a function from $$\mathbb{R} to$$ $$\mathbb{R}$$?

Accepted Answer

The set of ordered pairs $$\{(2,5), (3,6), (4,7)\}$$

Question 2

Given the equation $$x^2$$ + $$y^2 = 1$, does this equation define y$ as a function of x$?

Accepted Answer

No, because for some $$x$$ there are two possible $$y$$ values

Question 3

Find the domain of the function $$f(x) = \frac{1}{x-3}.$$

Accepted Answer

$$\mathbb{R} \setminus \{3\}$$

Question 4

Evaluate the function $$f(x) = 2x^2$ - 3x + 1 at$$ $$x = -2.$$

Accepted Answer

$$17$$

Question 5

Which of the following graphs passes the vertical line test and therefore represents $$y as a $$function of $$x$$?

Accepted Answer

A parabola opening upwards

Question 6

Let $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}. $$What is $$f(-3)$$?

Accepted Answer

$$9$$

Question 7

Given the graph of $$f(x)$$, which interval is $$f(x)$$ decreasing?

Accepted Answer

$$(-\infty, 0)$$

Question 8

Determine whether the function $$f(x) = x^3$ is even, odd, or neither.

Accepted Answer

Odd

Question 9

Find the difference quotient for $$f(x) = x^2$.

Accepted Answer

$$\frac{2x+h}{h}$$

Question 10

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

Accepted Answer

$$\mathbb{R}$$

Question 11

Let $$f(x) = \sqrt{x}$$ and $$g(x) = x - 2. $$What is the domain of $$f(g(x))$$?

Accepted Answer

$$x \geq 2$$

Question 12

Which pair of functions are inverses of each other?

Accepted Answer

$$f(x) = 2x$$, \quad g(x) = \frac{x}{2}$

Question 13

Use the horizontal line test to determine if $$f(x) = x^2$ has an inverse on $$\mathbb{R}$$.

Accepted Answer

No, because some horizontal lines intersect the graph more than once

Question 14

Find the inverse of $$f(x) = 3x + 2.$$

Accepted Answer

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

Question 15

Find the product of the complex numbers $$z_1 = 2 + 3i$ and z_2$ = 1 - 4i.$$

Accepted Answer

$$14 + 5i$$

Question 16

Simplify $$\sqrt{-16}.$$

Accepted Answer

$$4i$$

Question 17

Solve the quadratic equation $$x^2 - 5x + 6 = 0$ using factoring.

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 18

Find the vertex of the parabola $$y = x^2$ - 4x + 5.$$

Accepted Answer

$$(2, 1)$$

Question 19

A rectangular garden is to be fenced on three sides with 100 meters of fencing. What dimensions maximize the area?

Accepted Answer

Width $$= 25 m$$, Length $$= 50 m$$

Question 20

What is the end behavior of $$f(x) = -2x^4$ + 3x^2$ - 5 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Precalculus Exam 1 Study Guide: Functions, Polynomials, and Algebraic Concepts

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