Write in function?
2 Answers
To get my graphing package to show the valid points on the graph I used inequalities. So it is the blue line above the green area.
Explanation:
I suspect they are looking for you to calculate the 'critical point' which in the case is the y-intercept. This is at
Given:
Expand the expression inside of the absolute value:
Distribute the -1:
Combine like terms
Find the zeros of the quadratic:
Because the quadratic represents a parabola that opens downward, it is greater than or equal to zero within the domain,
This means that the absolute value function does nothing to the quadratic within this domain:
Outside of this domain, the absolute value function multiplies the quadratic by -1:
The above is the piecewise functional description of
The interval [0,2) is included in the last piece:
Here is a graph of this: