Determine the effects on the graph of the parent function f(x)=x+10 when g(x)=0.3f(x)

First, remember the definition of a vertical contraction/dilation.

If we have a function f(x), and we dilate it with a factor A, such as:

g(x) = A*f(x).

If A is larger than 1, then we are dilating the graph of f(x)

if A is smaller than 1, then we are contracting the graph of f(x).

In this case we have:

f(x) = x + 10 and g(x) = 0.3*f(x) = 0.3*x + 0.3*10 = 0.3*x + 3.

A = 0.3

then we have a contraction.

From this, we can conclude that the effects of this transformation in the graph will be that the graph of g(x) will be a vertical contraction of the graph of f(x).

(Where contracting means that in a given interval [x1, x2] the associated interval [f(x1), f(x2)] will be larger than [g(x1), g(x2)])

Below you can see both graphs, and see the difference between them, where green is f(x) and blue is g(x)

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