Question

How do you find the important points to graph `g(x)=2^x-3`?

Answer 1

see explanation

Explanation:

Set `y=2^x - 3`

At `y=0"; "2^x=3`

Taking logs

`xlog(2)=log(3) => x=log(3)/(log(2)) ~~1.58` to 2 decimal places
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At `x=0"; "y" "=" "2^0-3" " ->" "y" "=" " 1-3`

`y" "=" "-2`
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`Lim_(x->+oo)y= lim_(x->+oo)2^x-3 ->oo-3=oo`

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`Lim_(x->-oo) y=lim_(x->-oo)2^x-3 ->0-3=-3`

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