/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 19 Use a graphing utility to constr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 19

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=6^{-x}$$

Short Answer

Expert verified
The graph of the function starts out very high for negative x values and drops significantly as x increases, nearing but never reaching the x-axis.

Step by step solution

01

Constructing the table

Use a graphing utility to make some calculations. Start by plugging in various x-values such as \(-2, -1, 0, 1, 2\). For instance, for \(x = -2\), we have \(f(-2) = 6^{2} = 36\). For \(x = -1\), we have \(f(-1) = 6^{1} = 6\), for \(x = 0\), \(f(0) = 6^{0} = 1\), for \(x = 1\), \(f(1) = 6^{-1} = 1/6\), and for \(x = 2\), \(f(2) = 6^{-2} = 1/36\).
02

Plotting the points

With these calculated values, plot the points \((-2,36), (-1,6), (0,1), (1,1/6), (2,1/36)\) on a graph.
03

Sketching the graph

After plotting all of the points, trace out the curve that fits the points. This curve is the graph of the given function.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve the equation algebraically. Round your result to three decimal places. Verify your answer using a graphing utility. $$e^{-2 x}-2 x e^{-2 x}=0$$

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $f(x)=\log _{4} x$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{4} x-\log _{4}(x-1)=\frac{1}{2}$$

Is it possible for a logarithmic equation to have more than one extraneous solution? Explain.

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $$f(x)=\ln (x-4)$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.