Which of the following is the solution to | x -12 | < 15
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I will attach google sheet that I used to find regression equation.
We can see that linear fit does work, but the polynomial fit is much better.
We can see that R squared for polynomial fit is higher than R squared for the linear fit. This tells us that polynomials fit approximates our dataset better.
This is the polynomial fit equation:
I used h to denote hours. Our prediction of temperature for the sixth hour would be:
Here is a link to the spreadsheet (<span>https://docs.google.com/spreadsheets/d/17awPz5U8Kr-ZnAAtastV-bnvoKG5zZyL3rRFC9JqVjM/edit?usp=sharing)</span>
We can see that linear fit does work, but the polynomial fit is much better.
We can see that R squared for polynomial fit is higher than R squared for the linear fit. This tells us that polynomials fit approximates our dataset better.
This is the polynomial fit equation:
I used h to denote hours. Our prediction of temperature for the sixth hour would be:
Here is a link to the spreadsheet (<span>https://docs.google.com/spreadsheets/d/17awPz5U8Kr-ZnAAtastV-bnvoKG5zZyL3rRFC9JqVjM/edit?usp=sharing)</span>
Ok......... so ignore the pay part, that is not his pay but the 8% comission inclusive of the tax
The function is 
.
To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:
f(1)=1-11+36-36, not 0
f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).
Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).
We can also try some other factors of 36. Indeed we can check that
f(3)=27-99+108-36=135-135=0,
and
f(6)=216-396+216-36=0.
Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.
This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).
Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6.
The y-intercept is f(0), which is -36.
Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly,
we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.
Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity,
and it goes to minus infinity as x goes to - infinity.
To find the x-intercepts, we need to factorize the function. A very good idea is to first try the factors of 36:
f(1)=1-11+36-36, not 0
f(2)=8-44+72-36=-36+72-36=0. Here we have our first root (2).
Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).
We can also try some other factors of 36. Indeed we can check that
f(3)=27-99+108-36=135-135=0,
and
f(6)=216-396+216-36=0.
Thus, f(x)=(x-2)(x-3)(x-6). Note that if we expanded the right hand side expression, the constant term would be the product of the constants 2, 3, 6.
This is the reason why in the first place we looked at the factors of 36 for the possible zeros of f(x).
Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6.
The y-intercept is f(0), which is -36.
Note that f(0)<f(2) because f(0)=-36 and f(2)=0. This means that at the left side, the graph is coming from - infinity. Similarly,
we can check that f(10)=1000-1100+360-36=224> f(6). That is, to the right of our rightmost root, the graph is getting larger.
Thus, the end behaviors are: the graph goes to + infinity as x goes to + infinity,
and it goes to minus infinity as x goes to - infinity.