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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

What transformation takes fx15x3 to gx5x3 Question 1 options a horizontal compression by a factor 13 a translation 6 units right a horizontal stretch by a facto class=

Respuesta :

We can see that 
[tex]5x + 3 = 15( \frac{1}{3} x) + 3 = f( \frac{1}{3} x)[/tex]

So [tex]g(x) = f( \frac{1}{3} x)[/tex]

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. 
Kalahira
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.

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