- The function f(x) is defined piecewise, meaning it uses different formulas for different intervals of x.
- For x ≥ 0, use the formula f(x) = x + 1. This is a straight line with slope 1 and y-intercept 1, but you only graph it for x-values that are 0 or greater.
- For x < 0, use the formula f(x) = x - 3. This is a straight line with slope 1 and y-intercept -3, but you only graph it for x-values that are strictly less than 0.
- The inequalities (x ≥ 0 and x < 0) define the domain for each piece, telling you exactly where on the x-axis to draw each part of the graph.
- At x = 0, only the first piece applies (since 0 ≥ 0), so you plot the point (0, 1) from f(x) = x + 1. The second piece does not include x = 0, so there is no point from f(x) = x - 3 at x = 0.
- The result is a graph made of two separate rays: one starting at (0, 1) going right and up, and the other going left and down from just before x = 0, approaching but not including the point (0, -3).
Parent Tip: Review the logic above to help your child master the concept of piecewise.
