Question

The point (7,-2) is a point on the graph of y=f(x) what point must lie on: A) y=2f(x-4) B) y=-f(x)-4 C) y=f(-x) D) write the function that would shift (7,-2) right 3 then up 4

Answer 1

Answer:

a) The point that must lie on the functions;

$(11,-4)$

b) The point that must lie on the functions;

$(7,-2)$

Explanation:

Given that the point (7,-2) is a point on the graph of y=f(x).

We want to find the point that must lie on the functions;

a)

$y=2f(x-4)$$\begin{gathered} \frac{y}{2}=f(x-4) \\ \frac{y}{2}=-2 \\ y=-4 \\ x-4=7 \\ x=7+4=11 \\ x=11 \\ (11,-4) \end{gathered}$

The point that must lie on the functions;

$(11,-4)$

b)

$y=-f(x)-4$$\begin{gathered} y+4=-f(x) \\ -(y+4)=f(x) \\ x=7 \\ -(y+4)=-2 \\ y+4=2 \\ y=2-4 \\ y=-2 \\ (7,-2) \end{gathered}$

The point that must lie on the functions;

$(7,-2)$