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