Question

What is the effect on the graph of the function f(x)=c^2 when f(x) is changed to 3f(x-2)

Answer 1

The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²

Step-by-step explanation:

Let us revise the vertical stretch and the horizontal translation

• A vertical stretching is the stretching of the graph away from the x-axis
• If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by k.
• If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  
• If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  

∵ f(x) = x²

∵ f(x) is multiplied by 3

- 3 is greater than 1, then the graph of f(x) is stretched vertically

  by scale factor 3

∴ The graph of f(x) is stretched vertically by scale factor 3

∵ x² is changed to (x - 2)²

- That means the graph of f(x) translated 2 units to the right

∴ The graph of f(x) is translated 2 units to the right

The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²

Learn more:

You can learn more about transformation in brainly.com/question/2451812

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