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:

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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

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step-by-step explanation:

in english this is

ex.15 pag.85 create. write in ten lines the continuation of the ballad of the five motanasi, using verbs to the imperfect and to the perfect compound. five stars

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