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Which of the following equations represents a function that vertically stretches the parent function by a factor of two?

a. f(x) = 2x
b. f(x) = x^2
c. f(x) = 1/2x
d. f(x) = -2x

User David Buck
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1 Answer

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Final answer:

The equation that represents a function that vertically stretches the parent function by a factor of two is d. f(x) = -2x. However, it should be noted that this function also includes a reflection across the x-axis.

Step-by-step explanation:

The student is asking about a function that represents a vertical stretch of the parent function by a factor of two. A vertical stretch means that each y-value of the parent function is multiplied by the stretch factor, without affecting the x-values. Examining the given options:

  • a. f(x) = 2x: This function represents a straight line, and it does not vertically stretch a parent function by a factor of two; rather, it is a proportional change.
  • b. f(x) = x^2: This is the basic quadratic parent function without any vertical stretch.
  • c. f(x) = 1/2x: This function represents a vertical compression of the parent function f(x) = x by a factor of 1/2.
  • d. f(x) = -2x: This function includes a vertical stretch by a factor of two, but it also includes a vertical reflection across the x-axis due to the negative sign.

Therefore, the correct answer is d. f(x) = -2x, because it will increase the y-values of the parent function by a factor of two (a vertical stretch), but it also reflects the function.

User Guilherme Teubl
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