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.