Math Problem Statement

Complete the table for the function y = 0.25^x and graph the function.

Solution

It looks like you uploaded the same image again. Do you need additional clarification or help with the graphing part? Let me know how I can assist you!

Here’s a quick recap:

  • The function y=0.25xy = 0.25^x represents exponential decay.
  • The completed table is:
xxyy
-216
-14
01
10.25
  • You should plot at least two points from the table (e.g., (-1,4) and (0,1)) and then sketch a smooth curve that decreases towards zero as xx increases.

Would you like a step-by-step guide on how to plot the function?

Related Questions:

  1. How do you determine if a function is exponential growth or decay?
  2. What happens to the function if we change the base from 0.250.25 to 0.50.5?
  3. How does the function behave for very large and very small values of xx?
  4. What is the y-intercept of y=0.25xy = 0.25^x?
  5. How can we rewrite y=0.25xy = 0.25^x using base 2?

Tip: The function never reaches zero—it only gets closer and closer, forming a horizontal asymptote at y=0y = 0.

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Math Problem Analysis

Mathematical Concepts

Exponential Functions
Graphing
Exponential Decay

Formulas

y = a^x where 0 < a < 1 represents exponential decay

Theorems

Exponential functions have a horizontal asymptote at y = 0 for decay

Suitable Grade Level

Grades 8-10