suppose (-2,3) is on the graph of f(x).what point would be on g(x) if g(x) =-2f(x-3)+1
we know f(-2)=3
x-3 = -2 if x=1
g(1) = -2f(1-3)+1 = -2f(-2)+1 = -2(3)+1 = -5
So, (1,-5) is on the graph of g(x)
To find the point on the graph of g(x) using the point (-2, 3) on the graph of f(x), we need to substitute the x-coordinate of the given point into the equation for g(x).
Given:
f(x) = -2
Point on f(x): (-2, 3)
We are trying to find a point on g(x), where g(x) = -2f(x-3) + 1.
Step 1: Substitute the value of x into the equation for g(x).
g(x) = -2f(x-3) + 1
g(-2) = -2f(-2-3) + 1
Step 2: Substitute the given point (-2, 3) into f(x).
g(-2) = -2(3-3) + 1
Step 3: Simplify the expression inside the brackets.
g(-2) = -2(0) + 1
Step 4: Simplify further.
g(-2) = 0 + 1
g(-2) = 1
Therefore, the point on the graph of g(x) would be (-2, 1).