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Chapter 2: Problem 67
Determine whether each function is even, odd, or neither. $$f(x)=x^{2}-x^{4}+1$$
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Describe how to write the equation of a line if two points along the line are known.
The number of lawyers in the United States can be modeled by the function $$ f(x)=\left\\{\begin{array}{ll} 6.5 x+200 & \text { if } 0 \leq x<23 \\ 26.2 x-252 & \text { if } x \geq 23 \end{array}\right. $$ where \(x\) represents the number of years after 1951 and \(f(x)\) represents the number of lawyers, in thousands. In Exercises \(85-88,\) use this function to find and interpret each of the following. $$ f(50) $$
What must be done to a function's equation so that its graph is reflected about the \(y\) -axis?
Describe one advantage of using \(f(x)\) rather than \(y\) in a function's equation. 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. On the other hand, 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.
Begin by graphing the standard cubic function, \(f(x)=x^{3} .\) Then use transformations of this graph to graph the given function. $$ r(x)=(x-3)^{3}+2 $$
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