Dilation of function

Question

What kind of transformation converts the graph of f(x)=2x+1 into the graph of g(x)=4x+2

Answer 1

So if you look at function f(x) and then at g(x), you know that the function was transformed. In your title you know that it was a dilation. You should ask yourself, how did f(x) become g(x). Since you know it is a dilation, 1 of two things happened

1. The entire function was multiplied by something
2. a(2x+1)
3. This is a vertical stretch or compression
4. The input was multiplied by something
5. 2(a*x)+1
6. This is a horizontal stretch or compression

In this case, f(x) was doubled: 2(2x+1) = 4x+2

So we know this a vertical dilation.

Because the dilation factor (a or 2) is greater than 1, this is a vertical stretch by a factor of 2.