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The total distance is an illustration of a linear function.
<u>(1) Why the relationship is a function</u>
The relationship is a function because all input values of h, have exactly one corresponding output value of d
<u>(2) The function type</u>
The function is a discrete function, because the number of hours is an integer, and it cannot take decimal values (in this case)
<u>(3) The domain for a drive of 8 hours</u>
The domain is the set of time the girls drive.
So, the domain is: [0,8]
<u>(4) The range</u>
The function is given as:
When h = 0,
When h = 8,
So, the range is: [10,450]
<u>(5) The graph</u>
See attachment
<u>(6) The slope</u>
A linear function is represented as:
Where:
m represents the slope.
So, by comparison:
The slope in this case represents the distance travelled per hour
<u>(7) The y-intercept</u>
In (6) above, c represents the y-intercept.
So, by comparison:
The y-intercept in this case represents the initial distance
Read more about linear functions at
Let x represent the number.
.. x^2 +x = 2
.. x^2 +x +1/4 = 9/4 . . . . add 1/4 to complete the square
.. x +1/2 = ±3/2 . . . . . . . .square root
.. x = -2, 1
Numbers meeting that requirement are -2 and 1.
.. x^2 +x = 2
.. x^2 +x +1/4 = 9/4 . . . . add 1/4 to complete the square
.. x +1/2 = ±3/2 . . . . . . . .square root
.. x = -2, 1
Numbers meeting that requirement are -2 and 1.