Jamie and Hudson took a road trip to the beach. Their total distance traveled after getting on the highway can be found using the function d(h)=55h+10, where h is the number of hours they have been driving on the highway.

1) Explain why the relationship between total distance and hours is a function.

2) Is this function continuous or discrete? Explain how you know.

3) If the girls can drive a maximum of 8 hours, what is the domain for the function? Explain your answer.

4) If the girls can drive a maximum of 8 hours, what is the range for the function? Explain your answer.

5) Create a graph that models this function. Be sure to include a title and to label your x- and y-axis with the variable names, but just x and y.

6) What is the slope of the function? What does it represent?

7) What is the y-intercept? What does it represent?

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MrRoyal MrRoyal · Answer 1 · 2021-12-20T11:05:10+01:00

The total distance is an illustration of a linear function.

(1) Why the relationship is a function

The relationship is a function because all input values of h, have exactly one corresponding output value of d

(2) The function type

The function is a discrete function, because the number of hours is an integer, and it cannot take decimal values (in this case)

(3) The domain for a drive of 8 hours

The domain is the set of time the girls drive.

So, the domain is: [0,8]

(4) The range

The function is given as:

[tex]d = 55h +10[/tex]

When h = 0,

[tex]d = 55(0) +10 = 10[/tex]

When h = 8,

[tex]d = 55(8) +10 = 450[/tex]

So, the range is: [10,450]

(5) The graph

See attachment

(6) The slope

A linear function is represented as:

[tex]y = mx + c[/tex]

Where:

m represents the slope.

So, by comparison:

[tex]Slope = 55[/tex]

The slope in this case represents the distance travelled per hour

(7) The y-intercept

In (6) above, c represents the y-intercept.

So, by comparison:

[tex]c = 10[/tex]

The y-intercept in this case represents the initial distance