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 of $h (x) = - 2 {(x + 1)}^{3} + 3$ is

(b) Graph of $g (x) = | x + 4 | + 2$ is

Step by step solution

Step 1. Given data

GIven functions are

(a) $h (x) = - 2 {(x + 1)}^{3} + 3$

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

Step 2. Part (a)

Parent function of $h (x) = - 2 {(x + 1)}^{3} + 3$ is $f (x) = x^{3}$

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

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

Step 3. Graph of function

Plot the function $f (x) = x^{3}$ and transformed it into $h (x) = - 2 {(x + 1)}^{3} + 3$

Step 4. Pard (b)

Parent function of $g (x) = | x + 4 | + 2$ is $f (x) = | x |$

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

horizontal Shifting of $f (x)$ towards left by four units
Shift it vertically downwards by two units

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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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

Step by step solution

Step 1. Given data

Step 2. Part (a)

Step 3. Graph of function

Step 4. Pard (b)

Step 5. Graph of the function

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Graph each function using the techniques of shifting,compressing or stretching, and reflections. Start with thegraph of the basic function and show all stages.(a) h(x)=-2(x+1)3+3(b) g(x)=|x+4|+2

Short Answer

Step by step solution

Step 1. Given data

Step 2. Part (a)

Step 3. Graph of function

Step 4. Pard (b)

Step 5. Graph of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Discrete Mathematics

Geometry

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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