Q: What is the domain of the function $$f(x) = \sqrt{x^2$ - 8}$$?

$$x \leq -\sqrt{8}$$ \text{ or } x \geq \sqrt{8}$

Question 1

What is the domain of the function $$f(x) = \sqrt{x^2$ - 8}$$?

Accepted Answer

$$x \leq -\sqrt{8}$$ 	ext{ or } x \geq \sqrt{8}$

Question 2

Given $$g(x) = 2x^2$ - 5x$$, what is the domain of $$g(x)$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 3

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 4

If $$f(x) is an $$even function, which of the following must be true for all $$x in $$the domain?

Accepted Answer

$$f(-x) = f(x)$$

Question 5

The graph of $$y = f(x) + c$$ for $$c \u003e 0 is $$obtained by:

Accepted Answer

Shifting the graph of $$y = f(x) up$$ $$c$$ units

Question 6

How is the graph of $$y = f(x - c)$$ for $$c \u003e 0$$ related to the graph of $$y = f(x)$$?

Accepted Answer

Shifted right $$c$$ units

Question 7

Given $$f(x) = \frac{1}{x}$$, what is the equation of the vertical asymptote for $$f(x - 3)$$?

Accepted Answer

$$x = 3$$

Question 8

Which transformation results in the graph of $$y = -f(x)$$?

Accepted Answer

Reflection over the $$x-$$axis

Question 9

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

Accepted Answer

The graph of $$y = \sqrt{x}$$ reflected over the $$x-$$axis

Question 10

How do you sketch the graph of $$y = f(-x)$$ using the graph of $$y = f(x)$$?

Accepted Answer

Reflect the graph over the $$y-$$axis

Question 11

What is the effect of multiplying a function $$f(x) by a $$constant $$a \u003e 1$$?

Accepted Answer

Vertical stretch by a factor of $$a$$

Question 12

For $$0 \u003c a \u003c 1$$, what is the effect of multiplying $$f(x) by$$ $$a$$?

Accepted Answer

Vertical compression by a factor of $$a$$

Question 13

What is the domain of $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

$$x \geq \frac{5}{2}$$

Question 14

Which of the following describes the range of a function from its graph?

Accepted Answer

The set of all $$y-$$values from lowest to highest

Question 15

If $$f(x) is $$odd, which symmetry does its graph have?

Accepted Answer

Symmetry about the origin

Question 16

Which transformation is described by $$y = f(x) - c$$ for $$c \u003e 0$$?

Accepted Answer

Shift the graph of $$y = f(x)$$ down $$c$$ units

Question 17

Given $$f(x) = \sqrt{x}$$, what is the graph of $$y = \sqrt{-x}$$?

Accepted Answer

Reflect the graph of $$y = \sqrt{x}$$ over the $$y-$$axis

Question 18

Which of the following is a real-world example of a vertical stretch of a function?

Accepted Answer

Increasing the volume of a sound wave by multiplying its amplitude by 2

Question 19

A medical researcher models the growth of bacteria with $$f(x) = 2^x. If $$the researcher wants to model the effect of a drug that halves the population at every time $$x$$, which transformation should be applied?

Accepted Answer

Multiply $$f(x) by$$ $$\frac{1}{2}$$

Transformations and Properties of Functions in College Algebra

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