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what is the effect on the graph of f(x)=x^2 when it is transformed to h(x)=1/8x^2-13?
a.the graph of f(x) is vertically compressed by a factor of 8 and shifted 13 units to the right
b. the graph of f(x) is vertically compressed by a factor of 8and shifted 13 units down
c. the graph of f(x) is horizontally compressed by a factor of 8 and shifted 13 units down
d. the graph or f(x) is horizontally stretched by a factor of 8 and shifted 13 units to the right

please help!​

Sagot :

The transformation of a function may involve any change. The correct option is D.

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

  • Left shift by c units: y=f(x+c) (same output, but c units earlier)
  • Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

  • Up by d units: y = f(x) + d
  • Down by d units: y = f(x) - d

Stretching:

  • Vertical stretch by a factor k: y = k \times f(x)
  • Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)

The given function f(x)=x² is transformed to h(x)=(1/8)x^2-13, therefore, the graph or f(x) is horizontally stretched by a factor of 8 and shifted 13 units to the right.

Hence, the correct option is D.

Learn more about Transforming functions:

https://brainly.com/question/17006186

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Answer:

A.the graph of f(x) is vertically compressed by a factor of 8 and shifted 13 units to the right

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