Question

What transformation takes

Answer 1

We can see that 
$5x + 3 = 15( \frac{1}{3} x) + 3 = f( \frac{1}{3} x)$

So $g(x) = f( \frac{1}{3} x)$

When a function f(x) is transformed into f(ax) where |a| > 1, it's a horizontal compression by a factor of 1/a. But when a function f(x) is transformed into f(ax) where |a| < 1, it's a horizontal stretch by a factor of 1/a.

In this case, a = 1/3. So that's a horizontal stretch by a factor of 1/(1/3) = 3. Thus the answer choice is C. 

Answer 2

The transformation of f(x)=15x+3 to g(x)=5x+3 requires a horizontal compression by a factor of 1/3. f(x) has the has a y value of 18. g(x) has the y value of 8. Both lines share the x intersection of 3. When 15x is multiplied by 1/3, it becomes 5x, leaving g(x) with the same x intersection, but compressing the slope horizontally into a less steep line.