91Ó°ÊÓ

You will be developing functions that model given conditions. A car was purchased for \(\$ 22,500 .\) The value of the car decreased by \(\$ 3200\) per year for the first six years. Write a function that describes the value of the car, \(V\), after \(x\) years, where \(0 \leq x \leq 6 .\) Then find and interpret \(V(3)\).

What is a relation? Describe what is meant by its domain and its range.

Begin by graphing the cube root function, \(f(x)=\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$g(x)=\sqrt[3]{x-2}$$

What is the graph of a function?

A pet insurance policy has a monthly rate that is a function of the age of the insured dog or cat. For pets whose age does not exceed \(4,\) the monthly cost is 20 dollars . The cost then increases by 2 dollars for each successive year of the pet's age, CAN'T COPY THE GRAPH The cost schedule continues in this manner for ages not exceeding \(10 .\) The cost for pets whose ages exceed 10 is 40 dollars. Use this information to create a graph that shows the monthly cost of the insurance, \(f(x),\) for a pet of age \(x,\) where the function's domain is \([0,14]\)

Begin by graphing the cube root function, \(f(x)=\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$h(x)=-\sqrt[3]{x+2}$$

Explain how to identify the domain and range of a function from its graph.

Begin by graphing the cube root function, \(f(x)=\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$h(x)=-\sqrt[3]{x-2}$$

For people filing a single return, federal income tax is a function of adjusted gross income because for each value of adjusted gross income there is a specific tax to be paid. By contrast, the price of a house is not a function of the lot size on which the house sits because houses on same-sized lots can sell for many different prices. a. Describe an everyday situation between variables that is a function. b. Describe an everyday situation between variables that is not a function.

Suppose that a function \(f\) whose graph contains no breaks or gaps on \((a, c)\) is increasing on \((a, b),\) decreasing on \((b, c)\) and defined at \(b\). Describe what occurs at \(x=b\). What does the function value \(f(b)\) represent?