Question

Graph each exponential function. $$ y=6^{-x} $$

   Graph each exponential function.
$$
y=6^{-x}
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial ,… 5th Edition

Chapter 12, Problem 10

Instant Answer

Solved by Expert Amy Jiang

07/13/2020

Step 1

Step 1: First, we rewrite the function $y=6^{-x}$ as $y=(\frac{1}{6})^{x}$ to make it easier to work with. Show more…

Show all steps

lock

Thanks for your feedback!

Graph each exponential function. $$ y=6^{-x} $$

Play audio

Feedback

Powered by NumerAI

Amy Jiang and 58 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Negative Exponent and Reflection

A negative exponent in an exponential function, as seen in y = a^(-x), results in a horizontal reflection of the standard exponential graph y = a^x across the y-axis. This means that the behavior of the graph is mirrored horizontally, converting a growth function into a decay function or vice versa.

Horizontal Asymptote

Exponential functions typically have a horizontal asymptote, which is a line that the graph approaches but never touches. For most exponential functions, including those with a negative exponent, the horizontal asymptote is the x-axis (y = 0), indicating that the function's values get arbitrarily close to zero as x tends to positive or negative infinity.

Exponential Function

An exponential function is a function of the form f(x) = a^x, where 'a' is a positive constant. These functions are known for exhibiting rapid growth or decay depending on whether the base is greater than 1 or between 0 and 1. They are characterized by a constant ratio between successive values, which leads to their distinctive curved graph.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later