Lesson 18

Rewrite the rational function \(g(x) = \frac{x-4}{x}\) in the form \(g(x) = c + \frac{r}{x}\), where \(c\) and \(r\) are constants.

The average cost (in dollars) per mile for riding \(x\) miles in a cab is \(c(x)=\frac{2.5+2x}{x}\). As \(x\) gets larger and larger, what does the end behavior of the function tell you about the situation?

The graphs of two rational functions \(f\) and \(g\) are shown. One of them is given by the expression \(\frac{2-3x}{x}\). Which graph is it? Explain how you know.

Which polynomial function’s graph is shown here?

\(f(x)=(x+1)(x+2)(x+5)\)

\(f(x)=(x+1)(x-2)(x-5)\)

\(f(x)=(x-1)(x+2)(x+5)\)

\(f(x)=(x-1)(x-2)(x-5)\)

State the degree and end behavior of \(f(x)=5x^3-2x^4-6x^2-3x+7\). Explain or show your reasoning.

The graphs of two rational functions \(f\) and \(g\) are shown. Which function must be given by the expression of \(\frac{10}{x-3}\)? Explain how you know.