Math Problem Statement
What is the formula of g in terms of f? The graph below shows f as a solid blue line and g as a dotted red line. Choose from: A) f(-1/3x), B) f(-3x), C) f(3x), D) f(1/3x).
Solution
To determine the formula of in terms of , we need to analyze the graph carefully.
Observations:
- The graph of (solid blue line) is compared to (dotted red line).
- The red line appears compressed horizontally relative to . This suggests a horizontal scaling transformation.
- Horizontal transformations follow the rule:
where is a scaling factor:
- compresses horizontally.
- stretches horizontally.
Analyzing the Compression:
- On the graph, the solid blue line passes through points like and .
- The dotted red line reaches the same y-values as , but at scaled-down x-values.
To quantify this scaling:
- The blue curve at has the same y-value as the red curve at .
- This shows the x-values are scaled by a factor of .
Thus, the horizontal compression factor , and the transformation is:
Correct Answer:
The formula for in terms of is C: .
Do you want me to explain horizontal scaling further or have any questions?
Here are 5 related questions for practice:
- What happens to when it is transformed to ?
- How do you determine vertical transformations from a graph?
- What is the effect of on the graph of ?
- What is the difference between vertical and horizontal transformations?
- How can you identify a reflection in the -axis or -axis?
Tip: Horizontal transformations affect the input , while vertical transformations affect the output .
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Math Problem Analysis
Mathematical Concepts
Function Transformations
Horizontal Scaling
Graphs of Functions
Formulas
g(x) = f(kx)
Horizontal compression or stretch factor k
Theorems
Scaling transformations for functions
Suitable Grade Level
Grades 9-12