Function Decreasing Over Interval

nycguitarguy · 2024-04-14 15:24:57

Suppose that the function y = f(x) is decreasing on the interval (-2, 7).

A. Over what interval is the graph of y = f(x + 2) decreasing?

B. Over what interval is the graph of y = f(x - 5) decreasing?

nycguitarguy · 2024-04-15 10:38:51

Let me see.

For A

When x = -2, y = 0. The graph will start decreasing on the interval (-2, 0).

For B

When x = -2, y = -7. The graph will start decreasing on the interval (-2, -7).

Is this right?

Bob · 2024-04-15 19:42:45

f(x+2) moves the graph 2 places left. So the decreasing interval (-2,7) becomes (-4, 5).

Bob

nycguitarguy · 2024-04-16 09:36:33

Bob wrote:

f(x+2) moves the graph 2 places left. So the decreasing interval (-2,7) becomes (-4, 5).
Bob

You are a smart person for sure. Thank you.

nycguitarguy · 2024-04-19 09:28:48

Bob wrote:

f(x+2) moves the graph 2 places left. So the decreasing interval (-2,7) becomes (-4, 5).
Bob

Part A

For y = f(x + 2), the number 2 means the point (-2, 7) given for y = f(x) moves 2 units to the left.

Moving the given points 2 units to the left I get (-4, 5). The graph of y = f(x + 2) increases on the interval (-4, 5).

YOU SAY?

Part B

For y = f(x - 5), negative 5 moves the given points 5 units to the right.
Doing so, I get the point (3, 12).

I say the graph of y = f(x - 5) increases on the interval (3, 12).

YOU SAY?

Last edited by nycguitarguy (2024-04-20 02:01:28)

Bob · 2024-04-19 23:47:27

Part A fully correct.

Looks like a typo crept in for B . (3,12) was correct but then you put (3,10)

Bob

nycguitarguy · 2024-04-20 02:01:07

Bob wrote:

Part A fully correct.
Looks like a typo crept in for B . (3,12) was correct but then you put (3,10)
Bob

Yes, I made a typo. I will edit now.

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