91Ó°ÊÓ

For \(b>0,\) what are the domain and range of \(f(x)=b^{x ?}\)

Use the terms domain, range, independent variable, and dependent variable to explain how a function relates one variable to another variable.

What is the domain of a rational function?

Sketch a graph of \(y=x^{1 / 5}\).

Where is the tangent function undefined?

Graph of a linear function Find and graph the linear function that passes through the points \((1,3)\) and \((2,5)\).

The population of a small town was 500 in 2015 and is growing at a rate of 24 people per year. Find and graph the linear population function \(p(t)\) that gives the population of the town \(t\) years after \(2015 .\) Then use this model to predict the population in 2030.

Taxicab fees A taxicab ride costs \(\$ 3.50\) plus \(\$ 2.50\) per mile. Let \(m\) be the distance (in miles) from the airport to a hotel. Find and graph the function \(c(m)\) that represents the cost of taking a taxi from the airport to the hotel. Also determine how much it costs if the hotel is 9 miles from the airport.

a. Find the inverse of each function (on the given interval, if specified) and write it in the form \(y=f^{-1}(x)\) b. Verify the relationships \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\) $$f(x)=2 x$$

A taxicab ride costs \(\$ 3.50\) plus \(\$ 2.50\) per mile for the first 5 miles, with the rate dropping to \(\$ 1.50\) per mile after the fifth mile. Let \(m\) be the distance (in miles) from the airport to a hotel. Find and graph the piecewise linear function \(c(m)\) that represents the cost of taking a taxi from the airport to a hotel \(m\) miles away.