Question

PreCalc work, Need help with writing piece wise functions with graphs level 2. Giving branliest.

Answer 1

The piece-wise linear functions can be written as follows:

• $f(x) = -0.5x + 3, x < 5$.

• $f(x) = -5, x = 5$

• $f(x) = -x + 9, x > 5$.

What is a linear function?

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:

$f(x) = -0.5x + 3, x < 5$.

When x = 5, the function is constant at -5, hence:

$f(x) = -5, x = 5$

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:

$f(x) = -x + 9, x > 5$.

More can be learned about linear functions at brainly.com/question/25537936

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