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MATH133 Unit 4: Functions and Their Graphs
Individual Project Assignment: Version 2A
IMPORTANT: Please see Question 3 under Problem 2 for special instructions for this week’s IP assignment. This is mandatory.
Show all of your work details, explanations, and answers on the Unit 4 IP Answer Form provided. Problem 1: Children’s Growth years (144 months) has shown the following two equations. The function ℎ ? is the radical
A study of the data representing the approximate average heights of children from birth to 12 function representing the girls’ heights in inches after x months, and the function ℎ ? is the radical
function representing the boys’ heights in inches after x months (0 ≤ ? ≤ 144 months).
? = ℎ ? (?) = 3.08√ ? + 18.97
? = ℎ ? (?) = 2.87√ ? + 20.08
1. Choose five different values of x between 0 and 144 months, and calculate the values of each of of ? = ℎ ? (?) and ? = ℎ ? (?) in “t-tables” in the Answer Form supplied.
these functions for the chosen x values. Show all of your work and display these calculated values
2. Use these five different values of x and the corresponding calculated values of both functions, together with Excel or another graphing utility, to draw the graphs of these two functions. These graphs should be drawn on the same coordinate system so that the two functions can be easily compared. Insert those graphs into the Answer Form.
3. Set the two functions equal to each other, and solve the resulting radical equation for x. This value of x will be the age in months when boys and girls are the same height. (Show all of the steps for solving this radical equation on the Answer Form provided.)
4. What is the height in inches when boys and girls (according to these radical functions) are the same height? (Show all of your work on the Answer Form provided.)
5. What would be the average change in height for each of these radical functions between x = 25 and x = 36 months? (Show all of your work on the
Individual Project Assignment: Version 2A
IMPORTANT: Please see Question 3 under Problem 2 for special instructions for this week’s IP assignment. This is mandatory.
Show all of your work details, explanations, and answers on the Unit 4 IP Answer Form provided. Problem 1: Children’s Growth years (144 months) has shown the following two equations. The function ℎ ? is the radical
A study of the data representing the approximate average heights of children from birth to 12 function representing the girls’ heights in inches after x months, and the function ℎ ? is the radical
function representing the boys’ heights in inches after x months (0 ≤ ? ≤ 144 months).
? = ℎ ? (?) = 3.08√ ? + 18.97
? = ℎ ? (?) = 2.87√ ? + 20.08
1. Choose five different values of x between 0 and 144 months, and calculate the values of each of of ? = ℎ ? (?) and ? = ℎ ? (?) in “t-tables” in the Answer Form supplied.
these functions for the chosen x values. Show all of your work and display these calculated values
2. Use these five different values of x and the corresponding calculated values of both functions, together with Excel or another graphing utility, to draw the graphs of these two functions. These graphs should be drawn on the same coordinate system so that the two functions can be easily compared. Insert those graphs into the Answer Form.
3. Set the two functions equal to each other, and solve the resulting radical equation for x. This value of x will be the age in months when boys and girls are the same height. (Show all of the steps for solving this radical equation on the Answer Form provided.)
4. What is the height in inches when boys and girls (according to these radical functions) are the same height? (Show all of your work on the Answer Form provided.)
5. What would be the average change in height for each of these radical functions between x = 25 and x = 36 months? (Show all of your work on the