Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $2 f ( x + 1 ) - 3$
A) (4, 7)
B) (4, 14)
C) (4, 11)
D) (8, 11)

Question

Quizplus · Accepted Answer

Given a point (3, 7) on the graph of $f(x)$, to find a corresponding point on the graph of $2f(x + 1) - 3$, we substitute $x = 3$ into the transformed function. This gives us $2f(3 + 1) - 3 = 2f(4) - 3$. Since $f(3) = 7$, we don't directly know $f(4)$, but we can determine the effect of the transformation. The input to $f(x)$ is increased by 1, making the x-coordinate of the new point $3 + 1 = 4$. The output is doubled and then decreased by 3, so applying this to the y-coordinate, we get $2 \times 7 - 3 = 14 - 3 = 11$. Therefore, the new point is (4, 11).

Suppose (3, 7) Is a Point on the Graph Of f