How do you graph $y = 2^{- x}$ $y=2^-x$ ?

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How do you graph $y = 2^{- x}$ $y=2^-x$ ?

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Answer 1 · 2018-02-09T00:51:04

here is the graph
graph{2^-x [-10, 10, -5, 5]}

Explanation:

Start by changing $y = 2^{- x}$ $y=2^-x$ to $y = {(\frac{1}{2})}^{x}$ $y=(1/2)^x$ to have an untransformed graph.
Here are some characteristics of $y = {(\frac{1}{2})}^{x}$ $y=(1/2)^x$ to make sure you plot the points correctly:

-it will have y-intercept (0,1)

-the domain is all reals

-has $0 <$ $0<$ base $< 1$ $<1$

-is a decreasing function

-the horizontal asymptote is $y = 0$ $y=0$ , therefore the range is $y > 0$ $y>0$

To graph, start with the point (0,1) and multiply $y$ $y$ by $\frac{1}{2}$ $1/2$ to get the positive coordinates of $x$ $x$ . To get the negative coordinates of $x$ $x$ , start with (0,1) and multiply $y$ $y$ by 2. Keep in mind the restrictions and guidelines above.
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then graph accordingly making sure to get close to zero, but never actually reach it.

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How do you graph $y = 2^{- x}$ $y=2^-x$ ?

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