Question

Last PreCalc Question, Need help with writing piecewise functions with graphs. Giving brainliest!

Answer 1

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

• $f(x) = x, x \leq -2$.

• $f(x) = -x - 7, -2 < x \leq 1$.

• $f(x) = 2x - 9, x > 1$.

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 equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:

$f(x) = x, x \leq -2$.

For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:

$f(x) = -x - 7, -2 < x \leq 1$.

For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:

m = (-3 - (-5))(3 - 2) = 2.

The rule is:

y = 2x + b.

When x = 2, y = -5, hence:

-5 = 2(2) + b

b = -9.

Hence:

$f(x) = 2x - 9, x > 1$.

More can be learned about linear functions at brainly.com/question/24808124

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