Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
4th Edition
ISBN: 9781337687805
Author: James Stewart
Publisher: Cengage Learning
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Chapter T, Problem 4CDT

How are graphs of the functions obtained from the graph of f?

  1. (a) y = −f(x)
  2. (b) y = 2f(x) − 1
  3. (c) y = f(x − 3) + 2

(a)

Expert Solution
Check Mark
To determine

To find: The process to find the function y=−f(x) from the function f(x).

Explanation of Solution

According to the reflection of the function, the graph of the function y=−f(x) is obtained if the graph of y=f(x) is reflected vertically about x-axis.

Thus, the function y=f(x) has to be reflected in order to obtain the function y=−f(x).

(b)

Expert Solution
Check Mark
To determine

To find: The process to find the function y=2f(x)−1 from the function f(x).

Explanation of Solution

According to the magnification of the function the graph of the function y=kf(x) is obtained if the graph of y=f(x) is shrunken by k times.

Thus, the function y=2f(x) is obtained if the graph of y=f(x) is shrunken by k times.

According to the translation and reflection of the function the graph of the function y=f(x)+k is obtained if the graph of y=f(x) is translated upward by k units.

The graph of the function y=2f(x)−1 is obtained if the graph of y=2f(x) is translated downward by 1 units.

(c)

Expert Solution
Check Mark
To determine

To find: The process to find the function y=f(x−3)+2 from the function f(x).

Explanation of Solution

The graph of the function y=f(x−h) is obtained if the graph of y=f(x) is translated right by h units.

Thus, the graph of the function y=f(x−3) is obtained if the graph of y=f(x) is translated right by 3 units.

The graph of the function y=f(x)+k is obtained if the graph of y=f(x) is translated upward by k units.

Thus, the graph of the function y=f(x−3)+2 is obtained if the graph of y=f(x−3) is translated upward by 2 units.

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Chapter T, Problem 3CDT
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Chapter T, Problem 5CDT

Chapter T Solutions

Single Variable Calculus: Concepts and Contexts, Enhanced Edition

Ch. T - Evaluate each expression without using a...Ch. T - Simplify each expression. Write your answer...Ch. T - Expand and simplify. (a) 3(x + 6) + 4(2x 5) (b)...Ch. T - Factor each expression. (a) 4x2 25 (b) 2x2 + 5x ...Ch. T - Simplify the rational expression. (a) x2+3x+2x2x2...Ch. T - Rationalize the expression and simplify. (a) 1052...Ch. T - Rewrite by completing the square. (a) x2 + x + 1...Ch. T - Solve the equation. (Find only the real...Ch. T - Solve each inequality. Write your answer using...Ch. T - State whether each equation is true or false. (a)...
Ch. T - Prob. 1BDTCh. T - Prob. 2BDTCh. T - Prob. 3BDTCh. T - Prob. 4BDTCh. T - Sketch the region in the xy-plane defined by the...Ch. T - FIGURE FOR PROBLEM 1 1. The graph of a function f...Ch. T - If f(x) = x3, evaluate the difference quotient...Ch. T - Find the domain of the function. (a)...Ch. T - How are graphs of the functions obtained from the...Ch. T - Without using a calculator, make a rough sketch of...Ch. T - Let f(x)={1x2ifx02x+1ifx0 (a) Evaluate f(2) and...Ch. T - If f(x) = x2 + 2x 1 and g(x) = 2x 3, find each...Ch. T - Prob. 1DDTCh. T - Prob. 2DDTCh. T - Find the length of an arc of a circle with radius...Ch. T - Prob. 4DDTCh. T - Express the lengths a and b in the figure in terms...Ch. T - If sinx=13 and secy=54, where x and y lie between...Ch. T - Prove the identities. (a) tan sin + cos = sec ...Ch. T - Find all values of x such that sin 2x = sin x and...Ch. T - Sketch the graph of the function y = 1 + sin 2x...

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