Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. make sure to account for even and odd functions.
-when f(x) becomes f(x) + 2
-when f(x) becomes −(1 / 2) * f(x)

f(x) + 2 is translated 2 units up and -(1/2)*f(x) is reflected across x-axis.

Step-by-step explanation:

We have f(x) becomes f(x) + 2.

The y-intercept of f(x) is f(0), implies that y-intercept of f(x) + 2 is f(0) + 2. This means that the graph of f(x) is translated 2 units upwards.

Moreover, the region where f(x) increases will be the same region region where f(x) + 2 increases and there will not any change in the size of the figure.

Now, we have f(x) becomes -(1/2)*f(x).

The y-intercept of -(1/2)*f(x) is -(1/2)*f(0). This means that the graph is dilated by 1/2 units and then reflected across x-axis.

Moreover, the region where f(x) increases will be the opposite region region where -(1/2)*f(x)  increases and the size of the figure will change as dilation of 1/2 is applied to f(x)

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step-by-step explanation:

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