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
