Question

PLEASE I NEED HELP IM TERRIBLE AT FUNCTIONS AND HAVE POINTS TO OFFER

Let f(x)=6x. The graph of f(x) is transformed into the graph of g(x) by a vertical compression of 13 and a translation of 2 units up.
What is the equation for g(x)?
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g(x)=

Answer 1

Answer: g(x) = (6/13)x + 2.

Explanation:

To transform the graph of f(x) = 6x into the graph of g(x), we need to apply a vertical compression of 13 and a translation of 2 units up.

First, let's consider the vertical compression. A vertical compression with a factor of 13 means that the y-values of the graph will be multiplied by 1/13. So, we can write the equation for the vertical compression as:

g₁(x) = (1/13) * f(x)

Substituting the function f(x) = 6x, we have:

g₁(x) = (1/13) * 6x

= (6/13)x

Now, let's consider the translation 2 units up. To translate the graph up, we add 2 to the y-values of the graph. So, we can write the equation for the translation as:

g(x) = g₁(x) + 2

Substituting the function g₁(x) = (6/13)x, we have:

g(x) = (6/13)x + 2

Therefore, the equation for g(x) is g(x) = (6/13)x + 2.

Hope this helps.

Answer 2

The equation for g(x) is g(x) = (6x)/13 + 2.

Explanation:

To find the equation for the transformed function g(x), we can apply the given transformations to the original function f(x)=6x.

1. Vertical compression of 13: This means the graph is compressed vertically by a factor of 13. To achieve this, we divide the original function by 13.

f(x)/13 = (6x)/13

2. Translation of 2 units up: This means the graph is shifted 2 units upward. To achieve this, we add 2 to the function.

g(x) = (6x)/13 + 2

Therefore, the equation for g(x) is g(x) = (6x)/13 + 2.