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What can you say about the y-values of the two functions 𝑓(𝑥)=−5𝑥+2f(x)=−5 x +2 and 𝑔(𝑥)=−5𝑥2+2g(x)=−5x 2 +2 ?A.f(x) and g(x) have equivalent maximum y-values.B.g(x) has the largest possible y-value.C.The maximum y-value of f(x) approaches 2.D.f(x) has the largest possible y-value.SUBMITarrow_backPREVIOUS

Question

What can you say about the y-values of the two functions 𝑓(𝑥)=−5𝑥+2f(x)=−5 x +2 and 𝑔(𝑥)=−5𝑥2+2g(x)=−5x 2 +2 ?A.f(x) and g(x) have equivalent maximum y-values.B.g(x) has the largest possible y-value.C.The maximum y-value of f(x) approaches 2.D.f(x) has the largest possible y-value.SUBMITarrow_backPREVIOUS

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Solution

The function f(x) = -5x + 2 is a linear function, and its y-value will continue to decrease as x increases or decreases, so it does not have a maximum y-value.

On the other hand, the function g(x) = -5x^2 + 2 is a downward-opening parabola, and its maximum y-value occurs at the vertex of the parabola. In this case, the vertex is at x = 0, so the maximum y-value of g(x) is g(0) = 2.

Therefore, the correct answer is C. The maximum y-value of f(x) approaches 2.

This problem has been solved

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