Math Problem Statement

Which transformation is needed to graph the function g(x) = 3^x - 1? Choose the correct answer.

Solution

To answer the question in the image:

The given functions are:

  1. f(x)=3xf(x) = 3^x
  2. g(x)=3x1g(x) = 3^x - 1

The transformation from f(x)f(x) to g(x)g(x) involves subtracting 1 from the output of f(x)f(x). This means that the graph of f(x)f(x) is shifted 1 unit downward, as the subtraction affects the vertical position of the graph.

Correct answer: B. The graph of f(x)=3xf(x) = 3^x 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:

  1. How do vertical transformations differ from horizontal transformations?
  2. What would happen if you added 2 to 3x3^x instead of subtracting 1?
  3. How can you identify the horizontal asymptote for the transformed function g(x)g(x)?
  4. How does shifting downward affect the domain and range of g(x)g(x)?
  5. 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!

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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