Math Problem Statement
Below is the graph of y = |x|. Translate it to make it the graph of y = |x + 5| + 2.
Solution
The problem in the image asks to translate the graph of into . Let's break this down step by step.
-
Horizontal Shift:
- The term involves shifting the graph of 5 units to the left (opposite the sign inside the absolute value).
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Vertical Shift:
- Adding at the end means shifting the graph 2 units upward.
Translation Steps:
- Start with the graph of .
- Shift it 5 units to the left.
- Then shift it 2 units upward.
This will result in the graph of .
Would you like a detailed explanation of graph transformations or examples of similar problems?
Here are 5 related questions for further exploration:
- How would the graph change if the equation was ?
- What happens to the graph if is replaced with ?
- How does multiplying the absolute value, as in , affect the graph?
- Can you explain the general formula ?
- How would look compared to the current equation?
Tip: Always address horizontal transformations before vertical transformations for clarity in graph shifts.
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Math Problem Analysis
Mathematical Concepts
Graph Transformations
Absolute Value Functions
Horizontal and Vertical Shifts
Formulas
y = |x|
y = |x + h| + k
Theorems
Graph Translation Theorem
Suitable Grade Level
Grades 8-10