The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between x(height) and y(arm span) is sho
wn in the scatterplot below. The equation of the line of best fit modeling this relationship is given.
Y=4.5x + 0.977x
Mike is 175cm tall and George is 170cm tall.
Using the model, how many centimeters longer would we expect Mike's arm span to be than George's?
____Cm
Y=4.5x + 0.977x
Mike is 175cm tall and George is 170cm tall.
Using the model, how many centimeters longer would we expect Mike's arm span to be than George's?
____Cm
1 answer:
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Answers:
Functions
- y = -x+11
- y = 2x^2-6x+4
- y = -7
Not functions
- x = 3
- x^2+y^2 = 81
- y^2 = -5x-12
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Explanation:
A function is possible if and only if any given x input leads to exactly one y output.
For something like x^2+y^2 = 81, we can see that x = 0 leads to either y = 9 or y = -9. So this would <u>not</u> be a function. We would need x to pair with only y value to have it be a function.
We have the same thing going on with y^2 = -5x-12 as well.
For anything of the form x = k, where k is any real number, this is also not a function. We have one single input only and it leads to infinitely many outputs. So in a sense, this is even worse compared to the other examples.
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In summary, we have these three non-functions:
- x = 3
- x^2+y^2 = 81
- y^2 = -5x-12
Everything else is a function. You can use the vertical line test as a visual way to check.
