Starting with the function f(x) = e^x, create a new function by performing the following transformations. i. First shift the graph of f (x) to the lef

aflacatn 2020-11-27 Answered
Starting with the function \(f(x) = e^x\), create a new function by performing the following transformations.
i. First shift the graph of f (x) to the left by two units.
\(f_1 (x) =\)?
ii. Then compress your result by a factor of \(1/7\)
\(f_2 (x) =\) ?
iii. Next, reflect it across the x-axis.
\(f_3 (x) =\) ?
iv. And finally shift it up by eight units to create g (x).
g (x) =?

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Expert Answer

dieseisB
Answered 2020-11-28 Author has 3484 answers

The given function is \(f(x) = e^x\).
1.The graph of the function is shifted to the left by 2 units.
\(f_1(x)=f(x+h)\) h is the no of units shifted
=f(x+2)
\(=e^(x+2)\)
2.
the graph compressed by factor \(1/7\) as follows
\(f_2(x)=af(x)\)
\(=1/7e^x (0<1/7<1)\)
3.
Reflect the graph across x-axis
\(f_3(x)=-f(x)\)
\(=-e^x\)
4.The graph is shifted up by 8 units to create g(x)
\(g(x)e^x+8\) (8 units up)

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