Describe in words each combines transformation

Question

1) 5g(x)+6   2)-1/3h(x-6)+7

Answer 1

I will describe, in words, how basic function g(x) is transformed to give a new function, which I will call f(x).

f(x) = 5g(x)+6 is a transformation of g(x) achieved first by multiplying all output values of g(x) by 5, which can be called dilation by a factor 5, or a vertical stretch by a factor of 5.  Then, all y values are increased by 7, achieving a vertical shift upward by 7 units.

 

Second example: the graph of h(x) is shifted to the right 6 units, and then all its y-values are multiplied by one third (vertical compression), and then this new graph is reflected in the x-axis (all y values change to their opposites), and finally there's a vertical shift upward by 7 units.