Assume that f 4 1 Assume also that the graph of y fx Is sy

Assume that f(- 4) = 1. Assume also that the graph of y = f(x) Is symmetric with respect to the line x = - 2. Find another value for the function. Another value for the function is f(0) = 1.

Solution

the graph of y=f(x) is symmetric with respect to the line x=-2

and the x value for the given value f(-4)=1 is -4

-4 is at two units left from the line of symmetry x=-2

hence another x value must be at two units right from the line of symmetry

two units right means we have to add 2 to the x value of the line of symmetry

so the other x value would be at -2+2=0

and the y value must be the same for the symmetric point as the line of symmetry is a vertical line

so the y value will remain the same as the y value of the given value f(-4)=1 which is 1

hence we may conclude that another value for the function is f(0)=1