Question

the following data table represents a function.
a. identify the independent and dependent variables, and describe the domain and range.
b. make a clear graph of the function.
c. describe the function in words.

\

$$\begin{array}{|c|c|} \\hline \\text{speed (mi/hr)} & \\text{stopping distance (reaction plus braking in ft)} \\\\ \\hline 10 & 15 \\\\ 20 & 39 \\\\ 30 & 77 \\\\ 40 & 119 \\\\ 50 & 170 \\\\ 60 & 223 \\\\ 70 & 301 \\\\ \\hline \\end{array}$$

is stopping distance.
the domain of the function consists of all the speeds from the minimum value of 10 to the maximum value of 70.
the range of the function consists of all the distances from the minimum value of 15 to the maximum value of 301.
b. make a clear graph of the function. choose the correct graph below.

Explanation:

Identify variables and describe domain and range

Using the Independent and Dependent Variables and Domain and Range knowledge points

• Independent variable: Speed (mi/hr)
• Dependent variable: Stopping Distance (ft)
• Domain: All speeds from the minimum value of \(10\) to the maximum value of \(70\)
• Range: All distances from the minimum value of \(15\) to the maximum value of \(301\)

Analyze the correct graph representation

Using the Function Representation knowledge point

• The horizontal axis (x-axis) must represent the independent variable: Speed (mi/hr), ranging from \(0\) to \(70\).
• The vertical axis (y-axis) must represent the dependent variable: Distance (ft), ranging from \(0\) to \(350\).
• Let's check the data points: \((10, 15)\), \((20, 39)\), \((30, 77)\), \((40, 119)\), \((50, 170)\), \((60, 223)\), \((70, 301)\).
• The curve shows a progressive upward curvature (quadratic-like growth) because the differences between consecutive distance values increase as speed increases:
• \(39 - 15 = 24\)
• \(77 - 39 = 38\)
• \(119 - 77 = 42\)
• \(170 - 119 = 51\)
• \(223 - 170 = 53\)
• \(301 - 223 = 78\)
• Graph A shows a linear-like trend with a low slope, ending far below \(300\).
• Graph B has Speed on the vertical axis and Distance on the horizontal axis, which is incorrect.
• Graph C has Distance on the vertical axis, Speed on the horizontal axis, and correctly plots the points showing a curve bending upwards to end at \((70, 301)\).
• Graph D shows a decreasing trend, which is incorrect.
• Therefore, Graph C is the correct graph.

Answer:

Question 1

• The independent variable is speed.
• The dependent variable is stopping distance.
• The domain of the function consists of all the speeds from the minimum value of 10 to the maximum value of 70.
• The range of the function consists of all the distances from the minimum value of 15 to the maximum value of 301.

Question 2

• (A) Graph with linear trend
• (B) Graph with axes reversed
• (C) Graph with Distance on vertical axis, Speed on horizontal axis, showing an upward curve ending at (70, 301) (Correct answer)
• (D) Graph showing a decreasing trend