Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Exponentials and logarithms

Example 4 from Algebra and Trigonometry, 6.2 Graphs of Exponential Functions

Graphing the Stretch of an Exponential Function

Sketch a graph of $f (x) = 4 {(\frac{1}{2})}^{x} .$ State the domain, range, and asymptote.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
Before graphing, identify the behavior and key points on the graph.
- Since $b = \frac{1}{2}$ is between zero and one, the left tail of the graph will increase without bound as $x$ decreases, and the right tail will approach the x-axis as $x$ increases.
- Since $a = 4,$ the graph of $f (x) = {(\frac{1}{2})}^{x}$ will be stretched by a factor of $4.$
- Create a table of points as shown in Table 4.
  
  $x$ $- 3$ $4$ $- 1$ $0$ $1$ $2$ $3$
  
  $f (x) = 4 (\frac{1}{2})^{x}$ $32$ $16$ $8$ $4$ $2$ $1$ $0.5$
  
  Table 4
- Plot the y-intercept, $(0, 4),$ along with two other points. We can use $(- 1, 8)$ and $(1, 2) .$
Draw a smooth curve connecting the points, as shown in Figure 9.

Figure 9

The domain is $(- \infty, \infty);$ the range is $(0, \infty);$ the horizontal asymptote is $y = 0.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Sketch the graph of $f (x) = \frac{1}{2} {(4)}^{x} .$ State the domain, range, and asymptote.

How did it go?

PreviousApproximating the Solution of an Exponential Equation Next Writing and Graphing the Reflection of an Exponential Function

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.