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Chapter 7: Problem 25
Graph each equation in Exercises 21-32. Select integers for \(x\) from \(-3\) to 3 , inclusive. \(y=2 x+1\)
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The figure shows the healthy weight region for various heights for people ages 35 and older. If \(x\) represents height, in inches, and y represents weight, in pounds, the healthy weight region can be modeled by the following system of linear inequalities: $$ \left\\{\begin{array}{l} 5.3 x-y \geq 180 \\ 4.1 x-y \leq 140 \end{array}\right. $$ Use this information to solve Exercises 45-48. Is a person in this age group who is 5 feet 8 inches tall weighing 135 pounds within the healthy weight region?
Use a table of coordinates to graph each exponential function. Begin by selecting \(-2,-1,0,1\), and 2 for \(x\). \(y=2^{x+1}\)
a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 4 \\ \hline 1 & 5 \\ \hline 2 & 7 \\ \hline 3 & 11 \\ \hline 4 & 19 \\ \hline \end{array} $$
a. Determine if the parabola whose equation is given opens upward or downward. b. Find the vertex. c. Find the \(x\)-intercepts. d. Find the \(y\)-intercept. e. Use (a)-(d) to graph the quadratic function. \(y=-x^{2}+4 x-3\)
Each group member should consult an almanac, newspaper, magazine, or the Internet to find data that can be modeled by linear, exponential, logarithmic, or quadratic functions. Group members should select the two sets of data that are most interesting and relevant. Then consult a person who is familiar with graphing calculators to show you how to obtain a function that best fits each set of data. Once you have these functions, each group member should make one prediction based on one of the models, and then discuss a consequence of this prediction. What factors might change the accuracy of the prediction?
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