Question

Find a formula for the piecewise defined function with the given graph:

Answer 1

Can you pick two good points on the left line and tell me their coordinates?

Answer 2

I would guess they're (-1,-3) and (-5,-1)

Answer 3

I wish the grid was clearer. Hard to read the divisions. Even the x-axis does not quite align with the horizontal grid line.

Answer 4

I know. the grid line you're seeing is most likely from the backside of my paper. The graph I have shown has just a plain white background :/

Answer 5

Okay, we will just go with an estimate. It may not agree with their answer but at least you will learn the method. Find the equation of the line passing through (-1,-3) and (-5,-1).

Answer 6

hmm y=1/2x - 5/2?

Answer 7

You can do the arithmetic part later. Find the equation of the line and its domain will be restricted to -infinity < x < -1.

Answer 8

Then find the vertex of the parabola and find the equation of the parabola in vertex form.
Its domain is restricted to: -1 <= x <= 2

Answer 9

Then find the equation of the line on the right and its domain will be restricted to:
2 < x < infinity.

It is up to you whether you want to include x = 2 in the parabola and not in the straight line to the right OR not include it in the parabola but include it in the straight line. It does not matter either way because at x = 2 both have the same y-value.

Answer 10

ok, thanks for your help!

Answer 11

You are welcome.