Question

If the function y=e3x is vertically compressed by a factor of 4, reflected across the x-axis, and then shifted up 5 units, what is the resulting function? Write your answer in the form y=ceax+b.

Answer 1

The resulting function after vertically compressing, reflecting, and shifting the original function.

Step-by-step explanation:

To vertically compress a function by a factor of 4, we need to divide the original function by 4. So the resulting function is y=e^(3x)/4.

To reflect the function across the x-axis, we need to multiply the function by -1. So the resulting function is y=-e^(3x)/4.

To shift the function up 5 units, we need to add 5 to the function. So the final resulting function is y=-e^(3x)/4 + 5.

Answer 2

To vertically compress the function y=e3x by a factor of 4, reflect across the x-axis, and shift up 5 units, the resulting function is y=-e3(4x)+5.

Step-by-step explanation:

To vertically compress the function y=e3x by a factor of 4, we multiply the x-values by 4, resulting in y=e3(4x). To reflect across the x-axis, we replace y with -y, giving us y=-e3(4x). Lastly, to shift up 5 units, we add 5 to the y-values, giving us y=-e3(4x)+5.