Math Problem Statement
graph y = f(x+2)
Solution
To graph the function , follow these steps:
1. Understand the Transformation:
- The given function is a horizontal shift of the function .
- The inside the function causes a shift to the left by 2 units. This is because you subtract 2 from the -value of every point on the graph of to get the corresponding point on .
2. Plotting the Graph:
- Start with the graph of the original function .
- Shift each point on this graph 2 units to the left to obtain the graph of .
3. Example:
- Suppose the original function is . The graph is a parabola centered at the origin .
- To graph , shift the entire parabola left by 2 units. The new vertex will be at .
4. Sketching the Graph:
- Original Graph ( ): 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:
- How would the graph change if it were instead?
- What effect does a vertical shift have, such as ?
- How would you graph ?
- Can you explain how to combine horizontal and vertical shifts in a graph?
- How does the graph of compare to ?
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