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.

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.

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

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step-by-step explanation: