Q19. - Algebra 1

Question

PIZZA PARTY Katelyn ordered pizza and soda for her study group for $\mathbf{\$}\mathbf{38}$. The cost per person is given by $\mathit{y}\mathbf{=}\frac{38}{\mathbf{x}}$, where $\mathit{x}$ is the number of people in the study group. Graph the function and describe the asymptotes.

Step-by-Step Solution

Answer

The asymptotes of the given function are $\mathit{x}\mathbf{=}\mathbf{0}$ and $\mathit{y}\mathbf{=}\mathbf{0}$.

Step 1. Define asymptotes.

An asymptote is a line that the graph of a function approaches.

Step 2. Set a denominator equal to zero.

As division by zero is undefined, any value of a variable that results in a denominator of zero in a rational function is excluded from the domain of the function.

In $y=\frac{38}{x}$, the denominator cannot equal to zero, therefore, the vertical asymptote of the function is $x=0$ and the horizontal asymptote of the function is $y=0$.

Step 3. Graph the function.