Question

Algebra 2!! Which graph represents the following piecewise defined function?
-2x, x <-1
f(x) = -1,-1 x-1, x>2

Answer 1

The graph that defines the following piece-wise function is given by:

• f(x) = -2x, x < -1.

• $f(x) = -1, -1 \leq x < 2$.

• $f(x) = x - 1, x \geq 2$.

What is a piece-wise function?

It is a function that has different definitions based on the input.

In this problem, for x less than -1, the function is a line going through points (-1,2) and (-2,4), hence the slope is:

m = 4 - 2/(-2 - (-1)) = -2.

The slope of -2 means that it also passes through (0,0), hence the function is:

y = -2x.

For x between -1(inclusive) and 2(exclusive), it is a constant function at y = -1.

For x equal or greater than 2, the function is a line going through points (2,1) and (4,3), hence the slope is:

m = (3 - 1)/(4 - 2) = 1.

The slope of 1 means that the function passes through (0,-1), hence the function is:

y = x - 1.

Hence the piece-wise function is defined by:

• f(x) = -2x, x < -1.

• $f(x) = -1, -1 \leq x < 2$.

• $f(x) = x - 1, x \geq 2$.

More can be learned about piece-wise functions at https://brainly.com/question/24734454

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