How do you graph $y>2^x-4$ ?

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Answer 1 · 2016-12-15T17:30:50

Plot $y=2^x-4$ but with a dotted line.

The dotted line signifies that the value of y can never actually be $2^x-4$

Tony B Tony B

$color(blue)("Determine the key points")$

When $x=0" "ul("the dotted line")$ goes through $y=1-4=-3$

When $y=0" "ul("the dotted line")$ goes through $2^x=4=>x=2$

As $x$ increases a lot $2^x$ increases a lot and the influence of -4 from $y>2^x-4$ becomes less and less until it becomes isignificant.

$" "lim_(x-> +oo) y >lim_(x->oo)2^x -> oo$

As $x$ decreases it becomes negative so we have

$y>2^(-x)-4" "->" "y>1/(2^(+x))-4$ giving:

$" "lim_(x->-oo) y> lim_(x->oo) 1/(2^x) -4 ->-4$

How do you graph y>2^x-4y>2^x-4?