Question

What transformation takes

f(x)=15x+3 to g(x)=5x+3 ?

Question 1 options:

a horizontal compression by a factor 1/3


a translation 6 units right


a horizontal stretch by a factor of 3


a translation 6 units down

Answer 1

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.

Answer 2

We can see that

`5x + 3 = 15( (1)/(3) x) + 3 = f( (1)/(3) x)`

So
`g(x) = f( (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.