HELP PLZZ ASAP WILL GIVE 50 POINTS Adrienne said that a vertical stretch by a factor of 4, a horizontal shift to the left 1 unit, and a vertical shift down 3 units of the graph of the parent function f(x)=ex produce the graph of the function g(x)=4ex−1+3. Explain whether Adrienne is correct and, if not, determine the transformations that produce the graph of the function g(x)=4ex−1+3 from f(x)=ex.

known facts:

The graph of y=f(x−a), a>0

y=fx-a, a>0  

can be obtained by shifting graph y=f(x)

y=fx, a units right side of x-axis. The graph of y=f(x)+a, a>0 y= fx+ a,a>0

can be obtained by shifting graph y=f(x)

y=fx, a units upwards along y-axis.

Adrienne said:

a vertical stretch by a factor of 4, a horizontal shift to the left 1 unit and a vertical shift down 3 units of the graph of the parent function f(x)=ex

f(x)=e^x

produce the graph of the function g(x)=4ex−1+3

g(x)=4e^x-1+3.

by the above known facts, it can be concluded that

Adrienne is not correct

Step-by-step explanation:

i hope this helps you, i'm still doing it but i have to go for a min, one sec! <3

Adrienne is close, but she mixed up left and right

The x-1 in the exponent means we shift 1 unit right, and not left.

It's a bit confusing since it seems backwards.

But you can think of it like this: replacing x with x-1 shifts the xy axis 1 unit to the left, so we have the illusion the curve moved 1 unit to the right.

Here's one way to write out the transformation steps

f(x) = e^x

4*f(x) = 4*e^x vertical stretch by factor of 4

4*f(x-1) = 4*e^(x-1) ... shift 1 unit right

4*f(x-1)+3 = 4*e^(x-1)+3 ... shift 3 units up

g(x) = 4*e^(x-1)+3