Skip to main content
Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 4 - Inverse, Exponential, and Logarithmic FunctionsProblem 29
Chapter 5, Problem 29

Graph each function. ƒ(x) = (1/3)x

Verified step by step guidance
1
Recognize that the function given is an exponential function of the form \(f(x) = a^x\), where the base \(a = \frac{1}{3}\) is a positive number less than 1. This means the graph will represent exponential decay.
Create a table of values by choosing several values for \(x\), such as \(-2\), \(-1\), \(0\), \(1\), and \(2\). For each \(x\), calculate \(f(x) = \left(\frac{1}{3}\right)^x\) using the property of exponents.
Recall that for negative exponents, \(a^{-x} = \frac{1}{a^x}\). So, for example, \(f(-1) = \left(\frac{1}{3}\right)^{-1} = 3\), and \(f(-2) = \left(\frac{1}{3}\right)^{-2} = 9\).
Plot the points from your table on the coordinate plane. For example, plot \((0,1)\) since any number to the zero power is 1, and plot the other points accordingly.
Draw a smooth curve through the points, showing the exponential decay behavior: the graph approaches the \(x\)-axis (horizontal asymptote at \(y=0\)) but never touches it, and increases rapidly as \(x\) becomes more negative.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exponential Functions

An exponential function has the form f(x) = a^x, where the base a is a positive constant. The function grows or decays depending on whether a is greater than or less than 1. Understanding this helps in predicting the shape and behavior of the graph.
Recommended video:
6:13
Exponential Functions

Graphing Exponential Functions

Graphing involves plotting points by substituting values of x into the function and connecting them smoothly. Key features include the y-intercept at (0,1) and the horizontal asymptote, usually the x-axis, which the graph approaches but never touches.
Recommended video:
5:46
Graphs of Exponential Functions

Exponential Decay

When the base of an exponential function is between 0 and 1, the function represents exponential decay. This means the function decreases as x increases, approaching zero but never becoming negative, which affects the direction and shape of the graph.
Recommended video:
6:13
Exponential Functions
Related Practice
Textbook Question

Graph each function. See Example 2. ƒ(x) = (3/2)x

Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. limes, 1.6×\(\times\)10-2

Textbook Question

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 3(2)x-2 + 1 = 100

Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. grapefruit, 6.3×\(\times\)10-4

Textbook Question

Solve each equation. logx 25 = -2

1
views
Textbook Question

Determine whether each function graphed or defined is one-to-one. y = -(√x)+5

1
views