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The piece-wise linear functions can be written as follows:
.
.
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
.
When x = 5, the function is constant at -5, hence:
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
.
More can be learned about linear functions at brainly.com/question/25537936
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The regular monthly fee without coupon is $ 50
<em><u>Solution:</u></em>
Given that, Chelsey wants to join a fitness club
With the coupon, her total cost for the 6 months is $225
Therefore,
With coupon cost for 6 months = 225
She has a coupon that will give her $12.50 off the monthly rate for the first 6 months
Therefore,
For 6 months, coupon gives a off of,
Therefore,
Without coupon cost = 225 + 75 = 300
Thus the regular monthly fee without coupon is:
Thus regular monthly fee without coupon is $ 50