Question

Which graph shows the transformation of the function f(x)=e^x where the function is translated four units to the right, vertically compressed by a factor of 1/3, and translated down five units then translated five units down?

Answer 1

The graph that shows the transformation of the function f(x) = e^x is option D.

Step - by - Step Explanation

What to find? The transformation of the function f(x)=e^x.

Given:

• f(x) = 4^x

,

• Vertially compresses by a factor 1/3

,

• Translated four units to the right.

,

• Translated down five units.

Note that:

• If f(x) shifts up m- units, then we have f(x) + m.

,

• If f(x) shifts down n-units then we have f(x) - n.

,

• If f(x) shifts right p - units, then we have f(x - p).

,

• If f(x) shifts left q - units, then we have f(x+q).

From the given question, f(x) is translated four units to the right., hence e^x becomes eˣ⁻⁴

f(x) is further compressed by a factor of 1/3, the function becomes 1/3 eˣ⁻⁴.

Finally, the function is translated down five units, hence, the function becomes:

`f(x)=(1)/(3)e^(x-4)-5`

The graph of the function after the translation is