Pre calculus and calculus

Question

What kind of transformation converts the graph of 

f

(

x

)

=

4

x

+

7

 into the graph of 

g

(

x

)

=

x

+

7

?

Answer 1

f(x) = 4x + 7

f(x) = 4(x + 7/4) [I just factored out a "4"

So, now, to transform the function into g(x), vertically compress by a factor of 1/4 to turn it into:

y = x + 7/4

Now (since 7 = 28/4), translate the function up 21/4 units to yield:

y = x + 7/4 + 21/4 or

g(x) = x + 7