Question

Sketch the asymptotes and the graph of the function. Identify the domain and range. y = 7/x+4 -7Choose the correct graph below (the asymptotes are shown as red dashed lines).

Answer 1

In the horizontal asymptotes:

If the exponent of the numerator is the same as the exponent of the denominator, then:

`\begin{gathered} y=\text{ }(a)/(b) \\ y=\text{ }(7)/(1) \\ y=7 \end{gathered}`

But, when there's a translation, then y= k, which means y= - 7.

In the vertical asymptotes:

You have to equal the denominator to 0, so:

`\begin{gathered} x+\text{ 4= 0 } \\ x=\text{ -4} \end{gathered}`

The domain is all real numbers except -4 and the range is all real numbers except -7.

Now we have to check the graphs.

The correct graph is C. When x is -4 and y is -7.