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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

A vehicle increases its speed by

miles per hour every five minutes for two hours resulting in a maximum speed of 95 miles per hour. If f(x)

represents this function, what is the domain of

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

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

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

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

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

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

A vehicle increases its speed by

miles per hour every five minutes for two hours resulting in a maximum speed of 95 miles per hour. If f(x)

represents this function, what is the domain of

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

Correct answer:

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

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 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

Step 2: Use the information that describes f(x)

and create a graph that could possibly fit.

Let us identify the known information of the function.

is in intervals of "miles per every five minutes" and goes from zero to two hours. Therefore to find the units that the

-axis will have, convert two hours into minutes and then into intervals of five minutes.

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

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

The maximum speed is 95 miles per hour. Therefore, the

-axis spans from zero to 95.

At some value

the function reaches a maximum value of,

Since the question states, "A vehicle increases its speed by

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

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,

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

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 miles per hour every five minutes for 125 minutes resulting in a maximum speed of 35 miles per hour. If f(x) represents this function, what is the domain of ?

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

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

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

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

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

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

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

Correct answer:

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

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

Step 2: Use the information that describes f(x)

and create a graph that could possibly fit.

Let us identify the known information of the function.

is in intervals of "miles per every five minutes" and goes from zero to 125 minutes. Therefore to find the units that the

-axis will have, convert 125 minutes into intervals of five minutes.

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

Since the question states, "A vehicle starts to increase its speed after 25 minutes at a rate of

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

values that result in a real output that lies in the range of the function. In mathematical terms,

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

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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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