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.
oops, I forgot to give the function, that is f(x) =( 2^-2) - 2
The question is a bit confusing, could you please rewrite the question?
Is the question f(x)= (x^2-2) - 2?
My question is: Use transformations to graph the following function and submit a graph. Also state a) the domain, b) the range, c) the horizontal asymptote. f(x) = (2^-x) - 2. The -x is the exponent in the question.
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