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Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

A vehicle increases its speed by $\displaystyle x$ miles per hour every five minutes for two hours resulting in a maximum speed of 95 miles per hour. If $\displaystyle f(x)$ represents this function, what is the domain of $\displaystyle f$?

$\textup{Domain: }[5,120]$ $\displaystyle \textup{Domain: }[5,120]$

$\displaystyle \textup{Domain: }[0,120]$

$\textup{Domain: }[2,24]$ $\displaystyle \textup{Domain: }[2,24]$

$\displaystyle \textup{Domain: }[0,24]$

$\textup{Domain: }[5,95]$ $\displaystyle \textup{Domain: }[5,95]$

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All Common Core: High School - Functions Resources

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Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

$\textup{Domain: }[5,120]$ $\displaystyle \textup{Domain: }[5,120]$

$\displaystyle \textup{Domain: }[0,120]$

$\textup{Domain: }[2,24]$ $\displaystyle \textup{Domain: }[2,24]$

$\displaystyle \textup{Domain: }[0,24]$

$\textup{Domain: }[5,95]$ $\displaystyle \textup{Domain: }[5,95]$

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Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

Your answer:

$\textup{Domain: }[5,120]$ $\displaystyle \textup{Domain: }[5,120]$

Your answer:

$\displaystyle \textup{Domain: }[0,120]$

Your answer:

$\textup{Domain: }[2,24]$ $\displaystyle \textup{Domain: }[2,24]$

Your answer:

$\textup{Domain: }[5,95]$ $\displaystyle \textup{Domain: }[5,95]$

Correct answer:

$\displaystyle \textup{Domain: }[0,24]$

Explanation:

This particular question is testings one's ability to recognize characteristics of a function in terms of its context. Specifically, it is testing the ability to identify the domain of a function, or in other words, the possible input values that logically and mathematically work for the situation that is described by $\displaystyle f(x)$.

For the purpose of Common Core Standards, "relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes" falls within the Cluster B of "interpret functions that arise in applications in terms of the context" concept (CCSS.MATH.CONTENT.HSF-IF.B.5).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

This question is asking to find the domain, possible x values that make sense for this situation $\displaystyle f$.

Step 2: Use the information that describes $\displaystyle f(x)$ and create a graph that could possibly fit.

Let us identify the known information of the function.

$\displaystyle x$ is in intervals of "miles per every five minutes" and goes from zero to two hours. Therefore to find the units that the $\displaystyle x$-axis will have, convert two hours into minutes and then into intervals of five minutes.

$\displaystyle 2\textup{ hours}\times\frac{60\textup{ minutes}}{1\textup{ hour}}=\frac{120\textup{minutes}}{1}$

$\displaystyle 120\textup{ minutes}\times \frac{1\textup{ unit interval}}{5\textup{ minutes}}=24\textup{ unit interval}$

The maximum speed is 95 miles per hour. Therefore, the $\displaystyle y$-axis spans from zero to 95.

At some value $\displaystyle x$ the function reaches a maximum value of,

$\displaystyle f(x)=95$ .

Since the question states, "A vehicle increases its speed by $\displaystyle x$ miles per hour every five minutes for two hours", a linear relationship being time and speed is assumed.

Using the known information creates the graph below.

Step 3: Using the graph above, identify the domain.

Recalling that the domain of a function is the interval of $\displaystyle x$ values that result in a real output that lies in the range of the function. In the above graph the red line indicates the domain of the function. In mathematical terms,

$\displaystyle \textup{Domain: }[0,24]$.

Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

A vehicle starts to increase its speed after 25 minutes at a rate of $\displaystyle x$ miles per hour every five minutes for 125 minutes resulting in a maximum speed of 35 miles per hour. If f(x) $\displaystyle f(x)$ represents this function, what is the domain of $\displaystyle f$?

$\textup{Domain: }[5,15]$ $\displaystyle \textup{Domain: }[5,15]$

$\textup{Domain: }[5,25]$ $\displaystyle \textup{Domain: }[5,25]$

$\textup{Domain: }[5,30]$ $\displaystyle \textup{Domain: }[5,30]$

$\textup{Domain: }[0,25]$ $\displaystyle \textup{Domain: }[0,25]$

$\textup{Domain: }[10,25]$ $\displaystyle \textup{Domain: }[10,25]$

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Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

Your answer:

$\textup{Domain: }[5,15]$ $\displaystyle \textup{Domain: }[5,15]$

Your answer:

$\textup{Domain: }[5,30]$ $\displaystyle \textup{Domain: }[5,30]$

Your answer:

$\textup{Domain: }[0,25]$ $\displaystyle \textup{Domain: }[0,25]$

Your answer:

$\textup{Domain: }[10,25]$ $\displaystyle \textup{Domain: }[10,25]$

Correct answer:

$\textup{Domain: }[5,25]$ $\displaystyle \textup{Domain: }[5,25]$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

This question is asking to find the domain, possible x values that make sense for this situation $\displaystyle f$.

Step 2: Use the information that describes $\displaystyle f(x)$ and create a graph that could possibly fit.

Let us identify the known information of the function.

$\displaystyle x$ is in intervals of "miles per every five minutes" and goes from zero to 125 minutes. Therefore to find the units that the $\displaystyle x$-axis will have, convert 125 minutes into intervals of five minutes.

$\displaystyle 125\text{ minutes}\times\frac{1 \text{interval}}{5\text{minutes}}=25\text{ intervals}$

Since the question states, "A vehicle starts to increase its speed after 25 minutes at a rate of $\displaystyle x$ miles per hour every five minutes for 125 minutes", a linear relationship being time and speed is assumed.

Using the known information creates the graph below.

Step 3: Using the graph above, identify the domain.

Recalling that the domain of a function is the interval of $\displaystyle x$ values that result in a real output that lies in the range of the function. In mathematical terms,

$\displaystyle \textup{Domain: }[5,25]$.

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Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

All Common Core: High School - Functions Resources

Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

Flashcards: Graph's Domain: CCSS.Math.Content.HSF-IF.B.5

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