# 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

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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dieseisB

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)