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 31
Chapter 5, Problem 31

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

Verified step by step guidance
1
Identify the type of function given. Since the function is ƒ(x) = \(\left\)(\(\frac{3}{2}\)\(\right\))^x, it is an exponential function with base \(\frac{3}{2}\), which is greater than 1, indicating exponential growth.
Create a table of values by choosing several values for x (for example, -2, -1, 0, 1, 2) and calculate the corresponding y-values using the function ƒ(x) = \(\left\)(\(\frac{3}{2}\)\(\right\))^x. Remember to apply the exponent rules carefully.
Plot the points from the table on the coordinate plane. Each point will have coordinates (x, ƒ(x)) based on your calculations.
Draw a smooth curve through the plotted points, making sure the graph approaches the x-axis but never touches it (this is the horizontal asymptote y = 0), and that the curve increases as x increases because the base is greater than 1.
Label the graph with the function equation and the asymptote y = 0 to clearly show the behavior of the exponential function.

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 not equal to 1. It models growth or decay processes, and its graph shows rapid increase or decrease depending on the base. Understanding the behavior of exponential functions is essential for graphing them accurately.
Recommended video:
6:13
Exponential Functions

Plotting Points for Graphing

To graph a function like f(x) = (3/2)^x, calculate and plot points by substituting various x-values and finding corresponding y-values. This helps visualize the curve and identify key features such as intercepts and growth trends. Plotting points is a fundamental step in graphing any function.
Recommended video:
Guided course
04:29
Graphing Equations of Two Variables by Plotting Points

Asymptotes and End Behavior

Exponential functions have a horizontal asymptote, usually the x-axis (y=0), which the graph approaches but never touches. Understanding this helps predict the function's behavior for large positive or negative x-values, showing how the function grows or decays without bound.
Recommended video:
6:24
Introduction to Asymptotes
Related Practice
Textbook Question

Use a calculator to find an approximation to four decimal places for each logarithm. ln 144,000

Textbook Question

Graph each function. ƒ(x) = (1/3)x

7
views
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. log4 x = 3

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. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 2(1.05)x + 3 = 10

3
views