Question

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) − 3
When f(x) becomes −2 ⋅ f(x)

Can someone explain it to me. I dont know how to word it.

Answer 1

Answer:

f(x) - 3 is translated 3 units down and -2*f(x) is reflected across x-axis.

Step-by-step explanation:

We have, f(x) becomes f(x) - 3.

The y-intercept of f(x) is f(0), this implies y-intercept of f(x) -3 is f(0) - 3. This means that the graph of f(x) is translated 3 units down.

Next, we have f(x) becomes -2*f(x).

The y-intercept of -2*f(x) is -2*f(0) and it means that first the graph of f(x) is stretched horizontally by 2 units and then reflected across x-axis.

As, the function f(x) is multiplied by 2, this implies that resultant function -2*f(x) will be an even function and its graph will be symmetric about y-axis.

Moreover, the function -2*f(x) increases wherever f(x) decreases and vice-versa.

Answer 2

Answer:

f(x) is translated 3 units down and reflected across x-axis.

Step-by-step explanation:

Given : When f(x) becomes f(x) − 3  and  f(x) becomes −2 ⋅ f(x).

To find : 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.

Solution : We have given that :

f(x) becomes f(x) − 3  and  f(x) becomes −2 ⋅ f(x).

By the translation rule :

We have, f(x) becomes f(x) - 3.

The y-intercept of f(x) is f(0), this implies y-intercept of f(x) -3 is f(0) - 3. This means that the graph of f(x) is translated 3 units down.

Next, we have f(x) becomes -2*f(x).

The y-intercept of -2*f(x) is -2*f(0) and it means that first the graph of f(x) is stretched horizontally by 2 units and then reflected across x-axis.

As, the function f(x) is multiplied by 2, this implies that resultant function -2*f(x) will be an even function and its graph will be symmetric about y-axis.

Moreover, the function -2*f(x) increases wherever f(x) decreases and vice-versa

Therefore, f(x) is translated 3 units down and reflected across x-axis.