Math Problem Statement
Solution
The problem provides two functions:
It asks for the transformation that makes the graph of the image of the graph of .
To solve this:
- Substitute into :
- Simplify . Since , this can be written as:
- This simplification shows that , which represents a horizontal shift of the function .
Since , the transformation applied to is a horizontal shift 3 units to the right.
Would you like more details or further clarification?
Related Questions
- What would be the transformation if instead?
- How does a vertical shift affect the function ?
- What if instead? How would that change the graph?
- How would you express in terms of transformations?
- What effect does multiplying by a constant have on the graph?
Tip
For exponential functions, transformations involving addition or subtraction in the exponent affect the graph horizontally, while multiplications outside the function affect the graph vertically.
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
f(x) = 2^x
g(x) = f(x)/8
g(x) = 2^(x - 3)
Theorems
Properties of Exponential Functions
Transformation Rules for Functions
Suitable Grade Level
Grades 10-12
Related Recommendation
Graph Transformations of Exponential Functions: Reflection of f(x) = (9/2)^x to g(x) = -(9/2)^(-x)
Transforming the Graph of f(x) = 2^x to g(x) = -2^(x+1) + 5
Transformation of Exponential Function y = (1/2)^x
Graphing and Transforming Exponential Functions: Reflection of 8^x to 8^-x
Graph Transformation: Horizontal Compression for g(2x)