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a. Plot the graph on your grapher using the domain given. Sketch the result on your paper. b. Give the range of the function. c. Name the kind of function. d. Describe a pair of real-world variables that could be related by a graph of this shape. \(f(x)=2 x+3\) domain: \(0 \leq x \leq 10\)

Bacterial Culture Problem: When you grow a culture of bacteria in a petri dish, the area of the culture is a function of the number of bacteria present. Suppose that the area of the culture, \(A(t),\) measured in square millimeters, is given by this function of time, \(t,\) measured in hours: $$A(t)=9\left(1.1^{t}\right)$$ a. Find the area at times \(t=0, t=5,\) and \(t=10\) Is the area changing at an increasing rate or at a decreasing rate? How do the values of \(A(0), A(5),\) and \(A(10)\) allow you to answer this question? b. Assume that the bacteria culture is circular. Use the results of part a to find the radius of the culture at these three times. Is the radius changing at an increasing rate or at a decreasing rate? c. The radius of the culture is a function of the area. Write an equation for the composite function \(R(A(t))\) d. The radius of the petri dish is 30 mm. The culture is centered in the dish and grows uniformly in all directions. What restriction does this fact place on the domain of \(t\) for the function \(R \circ A ?\)

a. Plot the graph on your grapher using the domain given. Sketch the result on your paper. b. Give the range of the function. c. Name the kind of function. d. Describe a pair of real-world variables that could be related by a graph of this shape. \(g(x)=\frac{12}{x}\) domain: \(0

Mortgage Payment Problem: People who buy houses usually get a loan to pay for most of the house and pay on the resulting mortgage each month. Suppose you get a \(\$ 50,000\) loan and pay it back at \(\$ 550.34\) per month with an interest rate of \(12 \%\) per year \((1 \% \text { per month }) .\) Your balance, \(B\) dollars, after \(n\) monthly payments is given by the algebraic equation. $$B=50,000\left(1.01^{n}\right)+\frac{550.34}{0.01}\left(1-1.01^{n}\right)$$ a. Make a table of your balances at the end of each 12 months for the first 10 years of the mortgage. To save time, use the table feature of your grapher to do this. b. How many months will it take you to pay off the entire mortgage? Show how you get your answer. c. Plot on your grapher the graph of \(B\) as a function of \(n\) from \(n=0\) until the mortgage is paid off. Sketch the graph on your paper. d. True or false: "After half the payments have been made, half the original balance remains to be paid." Show that your conclusion agrees with your graph from part c. e. Give the domain and range of this function. Explain why the domain contains only integers.

a. Plot the graph using a window set to show the entire graph, when possible. Sketch the result b. Give the \(y\) -intercept and any \(x\) -intercepts and locations of any vertical asymptotes. c. Give the range. Quadratic (polynomial) function \(f(x)=x^{2}-6 x+40\) with the domain \(0 \leq x \leq 8\)

a. Plot the graph using a window set to show the entire graph, when possible. Sketch the result b. Give the \(y\) -intercept and any \(x\) -intercepts and locations of any vertical asymptotes. c. Give the range. Quartic (polynomial) function \(f(x)=x^{4}+3 x^{3}-8 x^{2}-12 x+16\) with the domain \(-3 \leq x \leq 3\)

Absolute Value Function - Odd or Even? Plot the graph of \(f(x)=|x| .\) Sketch the result. Based on the graph, is function \(f\) an odd function, an even function, or neither? Confirm your answer algebraically by finding \(f(-x)\)

Show that \(f(x)=\frac{1}{x}\) is its own inverse function.

a. Sketch a reasonable graph showing how the variables are related. b. Identify the type of function it could be (quadratic, power, exponential, and so on). The height of a punted football as a function of the number of seconds since it was kicked.

Explain why a function can have more than one \(x\) -intercept but only one \(y\) -intercept.