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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$$\begin{array}{|c|c|} \\hline \\text{speed (mi/hr)} & \\text{stopping distance (reaction plus braking in ft)} \\\\ \\hline 10 & 17 \\\\ 20 & 37 \\\\ 30 & 78 \\\\ 40 & 119 \\\\ 50 & 160 \\\\ 60 & 232 \\\\ 70 & 316 \\\\ \\hline \\end{array}$$

Explanation:

Identify variables

Using the Independent and Dependent Variables knowledge point

• The independent variable is the input that is controlled or varied: speed (in mi/hr).
• The dependent variable is the output that changes in response: stopping distance (in ft).

Determine domain definition

Using the Domain and Range knowledge point

• The domain represents all possible input values (independent variable).
• Since the independent variable is speed, the domain consists of all the speeds from the minimum value to the maximum value.

Find domain boundaries

Using the Domain and Range knowledge point

• Looking at the "Speed" column in the data table:
• Minimum speed value is \(10\).
• Maximum speed value is \(70\).
• Therefore, the domain consists of all the speeds from the minimum value of \(10\) to the maximum value of \(70\).

Answer:

a. 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>.