Math Problem Statement
Solution
To answer the question in the image:
The given functions are:
The transformation from to involves subtracting 1 from the output of . This means that the graph of is shifted 1 unit downward, as the subtraction affects the vertical position of the graph.
Correct answer: B. The graph of should be shifted 1 unit downward.
Would you like a detailed graphing explanation or more help with transformations?
Here are 5 questions to expand your understanding:
- How do vertical transformations differ from horizontal transformations?
- What would happen if you added 2 to instead of subtracting 1?
- How can you identify the horizontal asymptote for the transformed function ?
- How does shifting downward affect the domain and range of ?
- Could a graphing utility verify the transformation visually?
Tip: Always identify whether a transformation is horizontal or vertical by checking whether the change is applied inside or outside the function's main formula!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Exponential Functions
Transformations
Formulas
f(x) = 3^x
g(x) = 3^x - 1
Theorems
Graph transformations (vertical shift)
Suitable Grade Level
Grades 9-11
Related Recommendation
Determine the Transformation from f(x) = 2^x to g(x) = 2^x - 3
Exponential Function Transformation: Adjusting g(x)=(3^x)-3 for y-Intercept 0
Understanding Graph Shifts in Exponential Functions - f(x) = -3^(2x) - 4 vs. g(x) = -3^(2x)
Vertical Transformations of f(x) = 3^x to g(x) = 5(3^x) - 7
Vertical Shift of Exponential Function: f(x) = 3^x + 4 and g(x) = 3^x + 6