Question

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Answer 1

We are given the graph of a function and we are asked to determine the following:

VA (vertical asymptote). This is the value of "x" that the graph of the function doesn't touch. In this case, the VA is approximately x = -3.5

HA (horizontal asymptote) is the value of "y" that the graph of the function doesn't touch, in this case, the HA is y = 2.

The Domain of the function is the values of "x" that the function takes as input. Since the function takes all the values of "x" except the VA, the domain is:

`D=\mleft\lbrace x\in\R\parallel x\\e-3.5\mright\rbrace`

The range of the function is the values of "y" that the function yields. Since the function produces values for every "y" except the HA, the range is:

`R=\mleft\lbrace y\in\R\parallel y\\e2\mright\rbrace`