Question

graph the function. identify the x - and y - intercepts and the asymptotes of the graph. also, state the domain and range.
$y = -\frac{12}{x}$

select the correct graph below
\\(\bigcirc\\) a.
\\(\bigcirc\\) b.
\\(\bigcirc\\) c.
\\(\bigcirc\\) d.

identify the x - intercepts. select the correct answer below and, if necessary, fill in the answer box to complete your choice.
\\(\bigcirc\\) a. the x - intercept(s) is(are) \\(\square\\).
( type an ordered pair. use a comma to separate answers as needed. )
\\(\bigcirc\\) b. the function has no x - intercept.

Explanation:

Step1: Recall x-intercept definition

The x - intercept of a function is the point where \(y = 0\). So we set \(y=0\) in the function \(y =-\frac{12}{x}\) and solve for \(x\).

Step2: Solve for x when y = 0

Substitute \(y = 0\) into \(y=-\frac{12}{x}\), we get the equation \(0=-\frac{12}{x}\). Multiply both sides by \(x\) (assuming \(x
eq0\), because the original function is undefined at \(x = 0\)), we have \(0\times x=- 12\), which simplifies to \(0=-12\). This is a contradiction, so there is no solution for \(x\) when \(y = 0\).

Answer:

B. The function has no x - intercept.