The function f(x)=3g(x). which of the following shows possible graphs of f(x) and g(x)?

The answer is the first graph in the second raw

Step-by-step explanation:

* Lets study the dilation:

- 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 y-coordinates by k.

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

 by multiplying each y-coordinates by k.

* Notice that the "roots" on the graph stay in their same

 positions on the x-axis.

* Lets check our question:

∵ f(x) = 3g(x)

∵ f(x) = k.g(x)

∴ It is a vertical stretching or vertical compression

∵ k = 3 > 1

∴ It is vertical stretching with scale factor = 3

* That means we will multiply each y-coordinates in g(x) by 3

∴ The graph of f(x) will be away from x- axis and narrow to y- axis

∴ The answer is the first graph the second raw

Example: If g(x) = x²

                ∴ f(x) = 3x²

* Look to the graph:

- The red is the graph of g(x)

- The blue is the graph of f(x)

- f(x) = 3g(x)