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Chapter 2: Q. 10 (page 126)

Graph each function using the techniques of shifting,

compressing or stretching, and reflections. Start with the

graph of the basic function and show all stages.

(a) h(x)=-2(x+1)3+3

(b) g(x)=|x+4|+2

Short Answer

Expert verified

(a) graph ofh(x)=-2(x+1)3+3is

(b) Graph ofg(x)=|x+4|+2is

Step by step solution

01

Step 1. Given data

GIven functions are

(a) h(x)=-2(x+1)3+3

(b)g(x)=|x+4|+2

02

Step 2. Part (a)

Parent function of h(x)=-2(x+1)3+3is f(x)=x3

function role="math" localid="1645904280709" h(x)is obtained from f(x)by transformations-

  1. horizontal shifting of f(x)towards left by one unit
  2. its vertical stretch by a factor 2
  3. reflection of it about the y axis
  4. Shift it vertically upward by3units.
03

Step 3. Graph of function

Plot the function f(x)=x3and transformed it intoh(x)=-2(x+1)3+3

04

Step 4. Pard (b)

Parent function of g(x)=|x+4|+2isf(x)=|x|

the function g(x)is obtained from f(x)by transformations-

  1. horizontal Shifting of f(x)towards left by four units
  2. Shift it vertically downwards by two units
05

Step 5. Graph of the function

Plot the function f(x)=|x|and transformed it into g(x)=|x+4|+2

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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

True or False The cube function is odd and is increasing on the interval (-鈭�,鈭�).

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

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

1st50therms- \)0.33372/therm

Over 50therms- \(0.12360/therm

Gas charge- \)0.5038/therm

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

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

(c) Develop a model that relates the monthly charge Cfor xtherms of gas.

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

The domain of the variable in the expression x-3x+4is _________.
See all solutions

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