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What is the effect of a vertical stretch on the graph of a function?

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Question: What is the effect of a vertical stretch on the graph of a function?

Options:

  1. It compresses the graph towards the x-axis.
  2. It stretches the graph away from the x-axis.
  3. It shifts the graph to the left.
  4. It shifts the graph to the right.

Correct Answer: It stretches the graph away from the x-axis.

Solution: 

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, causing the graph to stretch away from the x-axis.

What is the effect of a vertical stretch on the graph of a function?

Practice Questions

Q1
What is the effect of a vertical stretch on the graph of a function?
  1. It compresses the graph towards the x-axis.
  2. It stretches the graph away from the x-axis.
  3. It shifts the graph to the left.
  4. It shifts the graph to the right.

Questions & Step-by-Step Solutions

What is the effect of a vertical stretch on the graph of a function?
  • Step 1: Understand that a function has input values (x) and output values (y).
  • Step 2: A vertical stretch means we are changing the output values (y) of the function.
  • Step 3: To perform a vertical stretch, we multiply the output values (y) by a number greater than 1.
  • Step 4: For example, if we have a function f(x), a vertical stretch by a factor of 2 would change it to 2 * f(x).
  • Step 5: This means that for every input x, the output y will be twice as high as it was before.
  • Step 6: As a result, the graph of the function will appear to stretch away from the x-axis, making it taller.
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