Math Problem Statement

graph y = f(x+2)

Solution

To graph the function y=f(x+2)y = f(x + 2), follow these steps:

1. Understand the Transformation:

  • The given function y=f(x+2)y = f(x + 2) is a horizontal shift of the function y=f(x)y = f(x).
  • The +2+2 inside the function causes a shift to the left by 2 units. This is because you subtract 2 from the xx-value of every point on the graph of y=f(x)y = f(x) to get the corresponding point on y=f(x+2)y = f(x + 2).

2. Plotting the Graph:

  • Start with the graph of the original function y=f(x)y = f(x).
  • Shift each point on this graph 2 units to the left to obtain the graph of y=f(x+2)y = f(x + 2).

3. Example:

  • Suppose the original function is y=f(x)=x2y = f(x) = x^2. The graph is a parabola centered at the origin (0,0)(0, 0).
  • To graph y=f(x+2)=(x+2)2y = f(x + 2) = (x + 2)^2, shift the entire parabola left by 2 units. The new vertex will be at (2,0)(-2, 0).

4. Sketching the Graph:

  • Original Graph ( y=f(x)y = f(x) ): Sketch this first if you have the function.
  • Shift Left: Move every point on the original graph 2 units to the left.

Would you like a specific example plotted or further details on any step?

5 Related Questions:

  1. How would the graph change if it were y=f(x2)y = f(x - 2) instead?
  2. What effect does a vertical shift have, such as y=f(x)+2y = f(x) + 2?
  3. How would you graph y=f(x+2)y = -f(x + 2)?
  4. Can you explain how to combine horizontal and vertical shifts in a graph?
  5. How does the graph of y=f(2x+4)y = f(2x + 4) compare to y=f(x+2)y = f(x + 2)?

Tip: Always check if the function's transformation involves multiple operations (e.g., stretching, reflecting) to ensure accurate graphing.

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Math Problem Analysis

Mathematical Concepts

Functions
Horizontal Shifts

Formulas

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Theorems

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Suitable Grade Level

High School