Question

PLZ HELP WORTH 25 PTS!!!!!

Consider the following piece-wise function.

How would the portion of the graph labeled "a" be defined?

(Answer choices are attached)

Answer 1

`\displaystyle y=- (1)/(2)x-3`

(first option)

Explanation:

Linear Functions

They can be defined by knowing two points on them or a point and the slope of the line. The portion "a" of the piecewise function must have these conditions, only by looking at the graph

* It must be decreasing, the slope must be negative

* It must be defined for x<-2, because for x>-2, the function is defined by another piece.

* It must pass through the point (-2,-2)

Options 2 and 4 are immediately discarded, since x>2

Testing it (-2,-2) belongs to

`\displaystyle y=- (1)/(2)x-3`

`\displaystyle y=- (1)/(2)(-2)-3=1-3=-2`

The point (-2,-2) belongs to this function, so it's the correct choice. Let's verify the last function

`\displaystyle y=- (1)/(2)x-6`

`\displaystyle y=- (1)/(2)(-2)-6=-5`

This is not the point we are testing, so the portion of the graph labeled "a" is

`\boxed{\displaystyle y=- (1)/(2)x-3}`

(First option)