/*! 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 16 Graph each function by making a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 16

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$h(x)=\left(\frac{1}{3}\right)^{x}$$

Short Answer

Expert verified
The graph of the function \(h(x) = (\frac{1}{3})^x\) is an exponential decaying function. It starts from high values on the left (for negative x-values), passes through (0,1), then approaches 0 as x increases. The points (-2,9), (-1,3), (0,1), (1,\(\frac{1}{3}\)), and (2,\(\frac{1}{9}\)) lie on the graph.

Step by step solution

01

Create a Table of Coordinates

To create the table of coordinates, choose a series of x-values and then calculate the corresponding y-values. In this case, let us choose the x-values to be -2, -1, 0, 1, 2. Using the function \(h(x) = (\frac{1}{3})^x\), the corresponding y-values are: \(h(-2) = (\frac{1}{3})^{-2} = 9, h(-1) = (\frac{1}{3})^{-1} = 3, h(0) = (\frac{1}{3})^{0} = 1, h(1) = (\frac{1}{3})^{1} = \frac{1}{3}, h(2) = (\frac{1}{3})^{2} = \frac{1}{9}\). So our table of coordinates will be: (-2,9), (-1,3), (0,1), (1,\(\frac{1}{3}\)), (2,\(\frac{1}{9}\)).
02

Draw the Graph

Now, plot these points on a graph and connect them with a smooth curve as this is an exponential function. Remember, exponential functions always have a horizontal asymptote (in this case is the x-axis) as the function approaches 0 for large negative x-values.
03

Confirm the Graph Using a Graphing Utility

Use a graphing calculator or an online graphing tool to plot the function \(h(x) = (\frac{1}{3})^x\) to confirm that the hand-drawn graph matches the machine-produced graph. Make sure the important points and the overall shape of the graph match.

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

Students in a mathematics class took a final examination. They took equivalent forms of the exam in monthly intervals thereafter. The average score, \(f(t),\) for the group after \(t\) months was modeled by the human memory function \(f(t)=75-10 \log (t+1), \quad\) where \(\quad 0 \leq t \leq 12 . \quad\) Use \(\quad\) a graphing utility to graph the function. Then determine how many months elapsed before the average score fell below 65.

Hurricanes are one of nature's most destructive forces. These low-pressure areas often have diameters of over 500 miles. The function \(f(x)=0.48 \ln (x+1)+27\) models the barometric air pressure, \(f(x),\) in inches of mercury, at a distance of \(x\) miles from the eye of a hurricane. Use this function to solve Exercises \(133-134\) The function \(W(t)=2600\left(1-0.51 e^{-0.075 t}\right)^{3}\) models the weight, \(W(t),\) in kilograms, of a female African elephant at age \(t\) years. (1 kilogram \(\approx\) 2.2 pounds) Use a graphing utility to graph the function. Then \([\text { TRACE }]\) along the curve to estimate the age of an adult female elephant weighing 1800 kilograms.

From 1970 through \(2010 .\) The data are shown again in the table. Use all five data points to solve Exercises \(70-74\). $$\begin{array}{cc}\hline \begin{array}{c}x, \text { Number of Years } \\\\\text { after } 1969 \end{array} & \begin{array}{c}y, \text { U.S. Population } \\\\\text { (millions) }\end{array} \\ \hline 1(1970) & 203.3 \\\11(1980) & 226.5 \\\21(1990) & 248.7 \\\31(2000) & 281.4 \\\41(2010) & 308.7 \end{array}$$ Use your graphing utility's power regression option to obtain a model of the form \(y=a x^{b}\) that fits the data. How well does the correlation coefficient, \(r,\) indicate that the model fits the data?

Solve each equation in Exercises \(146-148 .\) Check each proposed solution by direct substitution or with a graphing utility. $$(\log x)(2 \log x+1)=6$$

Evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: \(\log _{2} 32\) b. Evaluate: \(\log _{2} 8+\log _{2} 4\) c. What can you conclude about \(\log _{2} 32,\) or \(\log _{2}(8 \cdot 4) ?\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.