Math Problem Statement

3^x− 6/x draw graph of values -2<x<2.5 ​

Solution

Here is the graph of the function 3x6x3^x - \frac{6}{x} for the range 2<x<2.5-2 < x < 2.5. Notice the function is undefined at x=0x = 0, which is why there's a break in the curve.

Would you like more details on the behavior of this graph or the function?

Here are five related questions to explore further:

  1. What happens to the function as xx approaches 0 from the left and right?
  2. How does the graph behave for negative values of xx?
  3. Can we find the critical points of this function?
  4. What are the asymptotes of the function?
  5. How does this function compare to simpler exponential functions like 3x3^x?

Tip: For functions involving division by xx, always check how they behave near x=0x = 0 to spot discontinuities or asymptotes.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponential Functions
Rational Functions
Graphing

Formulas

f(x) = 3^x - 6/x

Theorems

Continuity and Discontinuity
Asymptotes

Suitable Grade Level

Grades 10-12