Math Problem Statement

Use the graph of the function f, plotted with a solid line, to sketch the graph of g(x) = f(x + 2).

Solution

The question asks you to use the graph of the function ff, which is plotted as a solid line, to sketch the graph of g(x)=f(x+2)g(x) = f(x + 2).

The transformation g(x)=f(x+2)g(x) = f(x + 2) represents a horizontal shift. In this case, the graph of f(x)f(x) is shifted to the left by 2 units because the +2+2 inside the function affects the xx-values, shifting the graph leftward.

Looking at the original graph of ff, which appears to be a parabola opening upward, the correct transformation would shift this parabola two units to the left.

Now, let's check the options:

  • Option A: This graph is shifted right, so it is incorrect.
  • Option B: This graph seems to be a leftward shift by 2 units, which looks correct.
  • Option C: This graph also appears to be a leftward shift, but it is shifted too far.
  • Option D: This graph is shifted right, which is incorrect.

So, the correct choice is Option B.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the effect of g(x)=f(xc)g(x) = f(x - c) on the graph of f(x)f(x)?
  2. How does a vertical shift differ from a horizontal shift in graph transformations?
  3. What happens if the transformation is g(x)=f(x2)g(x) = f(x - 2) instead?
  4. Can you explain how transformations affect the vertex of a parabola?
  5. How do you determine the direction of a shift based on the equation?

Tip: Remember that shifts inside the parentheses affect the graph horizontally, while those outside affect it vertically!

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Math Problem Analysis

Mathematical Concepts

Function Transformations
Horizontal Shifts
Graphing

Formulas

g(x) = f(x + c) shifts the graph of f(x) left by c units

Theorems

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Suitable Grade Level

Grades 8-10