# Can someone help me figure this question on functions and using transformations?Use transformations to graph the following function.  Also state a) the domain, b) the range, c) the horizontal...

Can someone help me figure this question on functions and using transformations?

Use transformations to graph the following function.  Also state a) the domain, b) the range, c) the horizontal asymptote.

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Given `f(x)=2^(-x)-2` :

(a) The domain is all real numbers. Exponentials accept any x as input.

(b) The range is y>-2. The value of `2^(-x)` goes to zero as x tends to infinity, so the limit of the function is -2.

Thinking in terms of transformations, we translate the graph of `y=2^(-x)` down 2 units. Since `y=2^(-x)` has a horizontal asymptote of y=0, the new horizontal asymptote is y=-2.

(c) The horizontal asymptote is y=-2.

(d) The base graph is `y=2^x` . Changing the x to -x results in a reflection across the y-axis, and subtracting 2 is a vertical translation down 2 units.

`y=2^x` in black;`y=2^(-x)` in green;`y=2^(-x)-2` in red.

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