Math Problem Statement

Describe the transformation that occurred: g(x) = f(x) - 1.

Solution

The question asks to describe the transformation that occurred for the function g(x)=f(x)1g(x) = f(x) - 1.

This transformation involves a vertical shift. The rule g(x)=f(x)1g(x) = f(x) - 1 indicates that the graph of f(x)f(x) has been shifted down by 1 unit.

Therefore, the correct answer is the "down 1" option.

Would you like more details on function transformations, or do you have any other questions?

Here are some related questions:

  1. What happens when the transformation is g(x)=f(x)+1g(x) = f(x) + 1?
  2. How do horizontal shifts differ from vertical shifts in function graphs?
  3. How would a transformation like g(x)=f(x)g(x) = -f(x) affect the graph?
  4. What kind of transformation does g(x)=2f(x)g(x) = 2f(x) represent?
  5. How would the graph change if the transformation was g(x)=f(x1)g(x) = f(x - 1)?

Tip: When a constant is added or subtracted outside the function, it results in a vertical shift.

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Math Problem Analysis

Mathematical Concepts

Function Transformations
Vertical Shift

Formulas

g(x) = f(x) - c

Theorems

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Suitable Grade Level

Grades 9-12