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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 4 (page 124)

Find the following for each function:
$f (x) = \sqrt{x^{2} - 4}$
Part (a): $f (2)$
Part (b): $f (- 2)$
Part (c): $f (- x)$
Part (d): $- f (x)$
Part (e): $f (x - 2)$
Part (f): $f (2 x)$

Short Answer

Expert verified

Part (a): $f (2) = 0$

Part (b): $f (- 2) = 0$

Part (c): $f (- x) = \sqrt{x^{2} - 4}$

Part (d): $- f (x) = - \sqrt{x^{2} - 4}$

Part (e): $f (x - 2) = \sqrt{x^{2} - 4 x}$

Part (f):localid="1645859836489" $f (2 x) = 2 \sqrt{x^{2} - 1}$

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

$f (x) = \sqrt{x^{2} - 4}$

Substitute $2$ in the given equation,

$f (2) = \sqrt{{(2)}^{2} - 4} f (2) = \sqrt{4 - 4} f (2) = 0$

02

Part (b) Step 1. Given information.

Consider the given function,

$f (x) = \sqrt{x^{2} - 4}$

Substitute $- 2$ in the given equation,

$f (- 2) = \sqrt{{(- 2)}^{2} - 4} f (- 2) = \sqrt{4 - 4} f (- 2) = 0$

03

Part (c) Step 1. Given information.

Consider the given function,

$f (x) = \sqrt{x^{2} - 4}$

Substitute $- x$ in the given equation,

$f (- x) = \sqrt{{(- x)}^{2} - 4} f (- x) = \sqrt{x^{2} - 4}$

04

Part (d) Step 1. Given information.

Consider the given function,

$f (x) = \sqrt{x^{2} - 4}$

From the question,

$- f (x) = - \sqrt{x^{2} - 4}$

05

Part (e) Step 1. Given information.

Consider the given function,

$f (x) = \sqrt{x^{2} - 4}$

Substitute $x - 2$ in the given equation,

$f (x - 2) = \sqrt{{(x - 2)}^{2} - 4} f (x - 2) = \sqrt{x^{2} + 4 - 4 x - 4} f (x - 2) = \sqrt{x^{2} - 4 x}$

06

Part (f) Step 1. Given information.

Consider the given function,

$f (x) = \sqrt{x^{2} - 4}$

Substitute $2 x$ in the given equation,

localid="1645859830755" $f (2 x) = \sqrt{{(2 x)}^{2} - 4} f (2 x) = \sqrt{4 x^{2} - 4} f (2 x) = \sqrt{4 (x^{2} - 1)} f (2 x) = 2 \sqrt{x^{2} - 1}$

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Most popular questions from this chapter

Graph $y = |x|$ . Then on the same screen graph $y = 2 |x|$ , followed by $y = 4 |x|$ , followed by

y = \frac{1}{2} |x|

.What pattern do you observe? Can you predict the graph of

y = \frac{1}{4} |x|

y = 5 |x|

?

In Problems 7鈥�18, match each graph to one of the following functions:

$A . y = x^{2} + 2 B . y = - x^{2} + 2 C . y = |x| + 2 D . y = - |x| + 2 E . y = {(x - 2)}^{2} F . y = - {(x + 2)}^{2} G . y = |x - 2| H . y = - |x + 2| I . y = 2 x^{2} J . y = - 2 x^{2} K . y = 2 |x| L . y = - 2 |x|$

match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

The slope of the line containing the points (-2, 3) and (3, 8) is ________.

The domain of $\frac{f}{g}$ consists of numbers $x$ for which $g (x)$ ____ $0$ that are in the domains of both ____ and ____.

See all solutions

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