Math Problem Statement

Describe the transformation from the parent function h(x) = 2^x to the transformed function j(x) = 2^x + 5.

Solution

The question involves identifying the transformation from the parent function h(x)=2xh(x) = 2^x to the transformed function j(x)=2x+5j(x) = 2^x + 5.

Explanation:

  • Parent function: h(x)=2xh(x) = 2^x
  • Transformed function: j(x)=2x+5j(x) = 2^x + 5

When we add a constant +5+5 to the function, it represents a vertical shift upwards by 5 units.

Correct Answer:

The parent function is transformed by Shifting Up 5.


Do you need further details on why this is the case, or have additional questions?

Here are 5 related questions to explore further:

  1. What happens if we subtract 5 instead of adding it?
  2. How does horizontal shifting differ from vertical shifting?
  3. How can we graphically see a shift upwards?
  4. What transformation occurs when we multiply by a negative constant?
  5. Can you explain the difference between vertical stretching and shifting?

Tip: Adding or subtracting from the function itself (outside the exponent) will always result in a vertical transformation.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponential Functions
Function Transformations

Formulas

h(x) = 2^x
j(x) = 2^x + 5

Theorems

Transformation of Functions

Suitable Grade Level

Grades 9-12