1. ## Absolute Value Question (Grade 11)

How do I find the rule?

2. level decreases at a constant rate ... H(n) is a linear function.

take two values for (n, H(n)) ...

(0, 86) (3, 68)

determine the slope ...

$\frac{\Delta H}{\Delta n} = \frac{68 - 86}{3 - 0} = -6$

use the point-slope form for a linear equation ...

H(n) - 86 = -6(n - 0)

H(n) = 86 - 6n

3. I'm still a little confused from your explanation.

4. Originally Posted by s3a
I'm still a little confused from your explanation.
What part is confusing you? Skeeter found the slope using two points and then, equation of line.

5. Is one of those points the vertex? Aren't those 3 points in a straight line; like I can't get the equations of two linear functions and find the vertex by finding their point of intersection if they're straight. Sorry if I've missed something, I'm a bit tired from studying all day.

6. what makes you think this problem involves an absolute value function?

7. My solution guide says:

f(x)=6|x-6|+50

but doesn't show work. I too had a problem figuring what it was at first but what else could it be?

8. the absolute value function accounts for the increase in the water level from the 6 month to the 12 month time period.

the function I completed works for the first 6 months only.

question should have stated that a bit more clearly.

9. Yes it really should have. You're the 3rd person it confused. Anyway, can you please show me how to do this in an absolute function way please so I can understand it because I am studying for an exam.

10. are you familiar with graphical transformations of the parent function y = |x| ?

11. You mean by adding the a,b,h,k paramaters? Yes, I am familiar with that.

12. having to find an absolute value function, I would sketch a graph with points at (0,86) (3,68) (6,50) (9,68) (12,86).

connecting the points using lines, one can see the large "V" indicating a transformed version of y = |x|.

slope is $\pm$ 6 ...

y = 6|x|

horizontal shift to the right 6 units ...

y = 6|x-6|

vertical shift up 50 units ...

y = 6|x-6| + 50

but, again, the problem statement should have been more clear in relating what was required as a solution.