Question

Describe the transformations of g(x)=-2f(x+4)

A) Reflection over x-axis
B) vertical compression x2
C) vertical stretch x2
D) left 4
E) right 4
F) up 4
G) down 4

Answer 1

Explanation:

the base function is f(x), right ?

so, now, going from left to right :

the "-" sign reflects everything over the x-axis (what was positive for f(x) is now negative for g(x) and vice versa).

the factor 2 makes the y- values twice as large for g(x) than for f(x). so, this is a vertical stretch of the factor 2.

and finally adding 4 to the original argument of f(x) as the new argument makes everything shift to the left by 4 units.

why ? the functional value of f(x) at e.g. x = 4 happens now for g(x) at x = 0.

in other words :

g(0) = f(0+4) = f(4)

g(1) = f(5)

...

so, all the functional values of f(x) are still happening for g(x), but at a smaller x (smaller by 4 units in this case).

therefore, the whole curve shifts to the smaller x-values (left).

therefore, the right answers are

A)

C)

D)