SOLUTION: Assume that f(2)=3. Assume also that the graph of y=f(x) is symmetric with respect to the line x=-3. Find another value for the function.

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Question 977329: Assume that f(2)=3. Assume also that the graph of y=f(x) is symmetric with respect to the line x=-3. Find another value for the function.
Answer by Edwin McCravy(20077)   (Show Source): You can put this solution on YOUR website!
Assume that f(2)=3. Assume also that the graph of y=f(x) is symmetric with respect to the line x=-3. Find another value for the function.
f(2)=3 means that when you substitute x=2 in the equation

y = f(x)

like this:

y = f(2)

That the value of y is 3 because f(2) = 3

That means that the graph contains the point (x,y) = (2,3)

So we plot that point (2,3) and the line x=-3, which is a vertical line 
through -3 on the x axis, the green line below:



We want to reflect that point across the green line.  Let's draw a dotted line
from that point (2,3) to the green line, like this:




We notice that the dotted line is 5 units.  So to reflect the point (2,3)
across the green line we extend the 5-unit dotted line 5 units to the left
of the green line like this:



So another point on the graph is (-8,3).

Answer: another value is f(-8)=3

[Recall that f(a)=b means that the point (a,b) is on the graph of f(x)]

The graph could look something line this: 



Edwin

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