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

The function f(x)=3g(x). Which of the following shows possible graphs of f(x) and-example-1
User AChampion
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Answer: the answer is b

Step-by-step explanation:i did the test yourself on algebra nation

User Meisterluk
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Answer:

The answer is the first graph in the second raw

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)

The function f(x)=3g(x). Which of the following shows possible graphs of f(x) and-example-1
User Nullable
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