Question 1

Which of the following best describes a function from set X into set Y?

Accepted Answer

A relation in which each x-value is associated with one y-value.

Question 2

Given the relation $$\{(4, 0), (1, 9), (0, -6), (-8, 3), (1, -2)\}$$, is this a function?

Accepted Answer

No, because the x-value 1 is paired with two different y-values.

Question 3

Which equation represents a function of $$x$$?

Accepted Answer

$$-x^2 + x + 6 + y = 0$

Question 4

What is the domain of $$f(x) = \frac{x+3}{x-5} in $$interval notation?

Accepted Answer

$$(-\infty, 5) \cup (5, \infty)$$

Question 5

Find the domain of $$f(x) = \sqrt{6x + 18}$$ using interval notation.

Accepted Answer

$$[3, \infty)$$

Question 6

What is the difference quotient for $$f(x) = x^2$ + 3$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Question 7

Which test is used to determine if a graph represents a function?

Accepted Answer

Vertical Line Test

Question 8

If $$f(x) = 2x^2$ - x - 1$$, what is the y-intercept of the graph?

Accepted Answer

$$-1$$

Question 9

For the piecewise function $$f(x) = \begin{cases} x^2$ & 	ext{if } -2 \leq x \u003c 0 \ x - 3 & 	ext{if } x \geq 0 \end{cases}$$, what is $$f(-1)$$?

Accepted Answer

$$1$$

Question 10

What is the basic function for the graph that passes through the origin and is symmetric about the y-axis?

Accepted Answer

$$f(x) = x^2$

Question 11

If $$f(x) = \sqrt{x}$$, what is the effect of the transformation $$f(x) = -\sqrt{x}$$?

Accepted Answer

The graph is reflected over the x-axis.

Question 12

What is the domain of $$f(x) = \frac{\sqrt{x}}{x-2}$$?

Accepted Answer

$$[0, 2) \cup (2, \infty)$$

Question 13

If $$f(x) = (x+3)^2$ - 2$$, what is the effect of the transformation $$+3 on $$the basic graph?

Accepted Answer

Shifts the graph left by 3 units.

Question 14

For $$f(x) = x^3$ - 16x$$, what are the x-intercepts?

Accepted Answer

$$x = 0, x = 4, x = -4$$

Question 15

Which of the following is NOT a reason for restricting the domain of a function?

Accepted Answer

Multiplication by zero

Question 16

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

Accepted Answer

$$(-\infty, \infty)$$

Question 17

What is the range of the basic function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 18

Which transformation results in a vertical stretch of the graph of $$f(x)$$?

Accepted Answer

$$y = af(x), a \u003e 1$$

Question 19

If $$f(x)$$ increases over an interval $$I of x-$$values, what must be true?

Accepted Answer

For any $$x_1$$ \u003c $$x_2 in$$ $$I$$, $$f(x_1$) \u003c f(x_2$)$$

College Algebra Study Guide: Functions and Their Graphs (Unit 1)

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