Given that (5,6) is on the graph of f(x), find the corresponding point for the function 4f(x)

The corresponding point for the function 4f(x) is (5 , 24)

Step-by-step explanation:

* Lets revise some transformation

- A vertical stretching: is the stretching of the graph away from

 the x-axis

- A vertical compression: is the squeezing of the graph toward

 the x-axis.

• if k > 1, the graph of y = k • f(x) is the graph of f (x) vertically

 stretched by multiplying each of its y-coordinates by k.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically compressed

 by multiplying each of its y-coordinates by k.

* In our problem:

- Point (5 , 6) is on the graph of f(x)

- The function will be 4f(x), that means vertical stretching

 or vertical compression

∵ k = 4

∵ 4 > 1

∴ It is a vertical stretch

∴ We will multiply the y-coordinate by 4

∴ y' = 4 × 6 = 24

* The corresponding point for the function 4f(x) is (5 , 24)