The graphed piece-wise function is:
y = x + 3 for x ≤ 0
y = 3 for x ≥ 0.
Which function is graphed?
We can see a piece-wise function, such that for x > 0 we have a constant at y = 3, and for x < 0 we have a line.
First, let's find the equation of the line. Remember that the general line is written as:
y = a*x + b
where a is the slope and b is the y-intercept.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁).
We can see that this line passes through (-3, 0) and (0, 3), then the slope is:
a = (3 - 0)/(0 - (-3)) = 1
And because it passes through the point (0, 3), we know that the y-intercept is b = 3, then the line is:
y = 1*x + 3
Now we can write the piece-wise function as:
y = x + 3 for x ≤ 0
y = 3 for x ≥ 0.
If you want to learn more about piece-wise functions, you can read:
https://brainly.com/question/3628123
