Math Problem Statement
apply a horizontal compression by a factor of 2 and a shift 5 units to the right to the equation y=x^4 + x^2
Solution
To apply the given transformations to the equation , follow these steps:
1. Horizontal compression by a factor of 2:
When applying a horizontal compression by a factor of 2, you replace with in the equation. This compresses the graph horizontally by a factor of 2.
So, the new equation becomes: Simplifying:
2. Horizontal shift 5 units to the right:
To shift the graph 5 units to the right, replace with in the equation.
Now the equation becomes:
Simplifying this:
Final equation:
This is the equation after applying the horizontal compression by a factor of 2 and a horizontal shift 5 units to the right.
Do you want more details or have any questions?
Here are 5 related questions you could explore:
- How do vertical compressions and stretches affect an equation?
- What is the difference between horizontal shifts and vertical shifts?
- How does a vertical shift by 3 units upwards change the equation?
- Can you apply both vertical and horizontal compressions at the same time?
- What happens to the graph of if you apply a horizontal stretch by a factor of 3?
Tip: Remember that horizontal transformations (shifts and compressions) act on the -variable, often in reverse of what you might expect! For example, shifting to the right involves subtracting from .
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Math Problem Analysis
Mathematical Concepts
Polynomial Functions
Transformations of Functions
Formulas
Horizontal compression by a factor of a: replace x with x/a
Horizontal shift by h units to the right: replace x with x - h
Theorems
Transformation Theorem: Horizontal stretches/compressions and shifts affect the input variable (x) in the reverse way expected.
Suitable Grade Level
Grades 10-12
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