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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. 3 (page 124)

Find the following for each function:
$f (x) = \frac{3 x}{x^{2} - 1}$
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): $f (2) = 2$

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

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

Part (d): $- f (x) = \frac{- 3 x}{- x^{2} + 1}$

Part (e): $f (x - 2) = \frac{3 (x - 2)}{x^{2} - 4 x + 3}$

Part (f): $f (2 x) = \frac{6 x}{4 x^{2} - 1}$

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

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

Substitute $x = 2$ in the given equation,

localid="1645858263721" $f (2) = \frac{3 (2)}{{(2)}^{2} - 1} f (2) = \frac{6}{4 - 1} f (2) = \frac{6}{3} f (2) = 2$

02

Part (b) Step 1. Given information.

Consider the given function,

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

Substitute $x = - 2$ in the given equation,

$f (- 2) = \frac{3 (- 2)}{{(- 2)}^{2} - 1} f (- 2) = \frac{- 6}{4 - 1} f (- 2) = \frac{- 6}{3} f (- 2) = - 2$

03

Part (c) Step 1. Given information.

Consider the given function,

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

Substitute $x = - x$ in the given equation,

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

04

Part (d) Step 1. Given information.

Consider the given function,

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

From the question,

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

05

Part (e) Step 1. Given information.

Consider the given function,

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

Substitute $x - 2$ in the given equation,

$f (x - 2) = \frac{3 (x - 2)}{{(x - 2)}^{2} - 1} f (x - 2) = \frac{3 (x - 2)}{x^{2} + 4 - 4 x - 1} f (x - 2) = \frac{3 (x - 2)}{x^{2} - 4 x + 3}$

06

Part (f) Step 1. Given information.

Consider the given function,

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

Substitute $2 x$ in the given equation,

$f (2 x) = \frac{3 (2 x)}{{(2 x)}^{2} - 1} f (2 x) = \frac{6 x}{4 x^{2} - 1}$

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Most popular questions from this chapter

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

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

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

True or False Every relation is a function.

In March $2011$ , Peoples Energy had the following rate schedule for natural gas usage in single- family residences:

Monthly service charge- $\(18.95$

Per therm service charge

$1 s t 50$ therms- $\) 0.33372 / t h e r m$

Over $50$ therms- $\(0.12360 / t h e r m$

Gas charge- $\) 0.5038 / t h e r m$

(a) What is the charge for using $50$ therms in a month?

(b) What is the charge for using $500$ therms in a month?

(c) Develop a model that relates the monthly charge $C$ for $x$ therms of gas.

(d) Graph the function found in part (c)

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

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

See all solutions

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