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

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

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Answer 1 · 2016-10-15T15:10:11

see explanation

Explanation:

Tony B

Set $y = 2^{x} - 3$ $y=2^x - 3$

At $y = 0; 2^{x} = 3$ $y=0"; "2^x=3$

Taking logs

$x log (2) = log (3) \Rightarrow x = \frac{log (3)}{log (2)} \approx 1.58$ $xlog(2)=log(3) => x=log(3)/(log(2)) ~~1.58$ to 2 decimal places
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At $x = 0; y = 2^{0} - 3 \to y = 1 - 3$ $x=0"; "y" "=" "2^0-3" " ->" "y" "=" " 1-3$

$y = - 2$ $y" "=" "-2$
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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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How do you find the important points to graph $g (x) = 2^{x} - 3$ $g(x)=2^x-3$ ?

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