Question

Sketch the graph of the given equation. $$ y=e^{|x|} $$

   Sketch the graph of the given equation.
$$
y=e^{|x|}
$$

Calculus Single Variable

Calculus Single Variable

Brian E. Blank,… 2nd Edition

Chapter 2, Problem 74

Instant Answer

Solved by Expert Christopher Stanley

03/02/2022

Step 1

If x is positive or zero, |x| = x. If x is negative, |x| = -x. Show more…

Show all steps

lock

Thanks for your feedback!

Sketch the graph of the given equation. $$ y=e^{|x|} $$

Play audio

Feedback

Powered by NumerAI

Christopher Stanley and 53 other subject Calculus 1 / AB 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

Exponential Functions

Exponential functions are mathematical functions in which the variable appears in the exponent. They show rapid growth or decay and are defined for all real numbers. Understanding their behavior, such as the rate of increase and the presence of horizontal asymptotes, is fundamental in graph analysis.

Absolute Value Functions

Absolute value functions return the non-negative magnitude of a number, making them inherently non-negative. When used inside another function, absolute value can alter the function’s input by reflecting negative inputs to positive ones, effectively combining behaviors of a function over mirrored intervals.

Symmetry in Graphs

Graph symmetry, particularly even symmetry, occurs when a function satisfies f(x) = f(-x) for all x in its domain. This concept is crucial for functions with an absolute value in the input, as it results in a mirror image of the graph across the y-axis.

Piecewise Function Analysis

Piecewise function analysis involves breaking the function into parts based on the behavior of the absolute value. By considering the cases where the input is non-negative and where it is negative, one can analyze and sketch the overall graph by combining the distinct behaviors into a cohesive picture.

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