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Consider the following scenario: Barbara decides to take a walk. She leaves home, walks 2 blocks in 5 minutes at a constant speed, and realizes that she forgot to lock the door. So Barbara runs home in 1 minute. While at her doorstep, it takes her 1 minute to find her keys and lock the door. Barbara walks 5 blocks in 15 minutes and then decides to jog home. It takes her 7 minutes to get home. Draw a graph of Barbara's distance from home (in blocks) as a function of time.

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ f(x)=-\sqrt[3]{x} $$

Determine algebraically whether each function is even, odd, or neither. \(h(x)=\frac{-x^{3}}{3 x^{2}-9}\)

Find the following for each function: (a) \(f(0)\) (b) \(f(1)\) (c) \(f(-1)\) (d) \(f(-x)\) (e) \(-f(x)\) (f) \(f(x+1)\) (g) \(f(2 x)\) (h) \(f(x+h)\) \(f(x)=|x|+4\)

Determine algebraically whether each function is even, odd, or neither. \(F(x)=\frac{2 x}{|x|}\)

Consider the following scenario: Jayne enjoys riding her bicycle through the woods. At the forest preserve, she gets on her bicycle and rides up a 2000 -foot incline in 10 minutes. She then travels down the incline in 3 minutes. The next 5000 feet is level terrain, and she covers the distance in 20 minutes. She rests for 15 minutes. Jayne then travels 10,000 feet in 30 minutes. Draw a graph of Jayne's distance traveled (in feet) as a function of time.

If \(f(x)=\operatorname{int}\left(\frac{x}{2}\right),\) find (a) \(f(1.2)\) (b) \(f(1.6)\) (c) \(f(-1.8)\)

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ f(x)=-\sqrt{x} $$

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, \(y=x^{2}\) ) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. $$ f(x)=2(x+1)^{2}-3 $$

Find the following for each function: (a) \(f(0)\) (b) \(f(1)\) (c) \(f(-1)\) (d) \(f(-x)\) (e) \(-f(x)\) (f) \(f(x+1)\) (g) \(f(2 x)\) (h) \(f(x+h)\) \(f(x)=\frac{2 x+1}{3 x-5}\)