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.

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

a. the independent variable is speed and 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 from the minimum value of to the maximum value of .

Explanation:

Identify variables

Using the Independent and Dependent Variables knowledge point, we analyze the relationship in the data table. The stopping distance depends on the speed of the vehicle. Therefore, the independent variable is speed, and the dependent variable is stopping distance.

Determine domain

Using the Domain and Range knowledge point, the domain represents all possible input values (independent variable). From the table, the speed values range from a minimum of \(10\) to a maximum of \(70\). Thus, the domain consists of all the speeds from the minimum value of \(10\) to the maximum value of \(70\).

Determine range

Using the Domain and Range knowledge point, the range represents all possible output values (dependent variable). From the table, the stopping distance values range from a minimum of \(15\) to a maximum of \(301\). Thus, the range consists of all the stopping distances from the minimum value of \(15\) to the maximum value of \(301\).

Answer:

The independent variable is <blank>speed</blank> and the dependent variable is <blank>stopping distance</blank>.

The domain of the function consists of all the <blank>speeds</blank> from the minimum value of <blank>10</blank> to the maximum value of <blank>70</blank>.

The range of the function consists of all the <blank>stopping distances</blank> from the minimum value of <blank>15</blank> to the maximum value of <blank>301</blank>.