Graphing Polynomial Functions with Absolute Value Variables
Graph the following function: f(x) = x² + |x| Create two cases. One where x ≥ 0, and another where x < 0. Case 1: when x ≥ 0 If x ≥ 0, then the absolute value variable will remain positive, where the function will only apply to the positive x-axis, its domain. g(x) = x² + x Case 2: when x < 0 If x < 0, then the absolute value variable will become negative, where the function will only apply to the negative x-axis, its domain. h(x) = x² - x Graph both functions on the same Cartesian plane keeping in mind of their domains.
g(x) when simplified gives us two zeros: one at (0,0) and the other at (-1,0). Since g(x)'s domain is only when x ≥ 0, it cannot pass further on after the zero at the origin, (0,0). h(x) when simplified gives us two zeros: one at (0,0) and the other at (1,0). Since h(x)'s domain is only when x < 0, it cannot pass further on after the zero at the origin, (0,0). Graph the following function: f(x) = x² - |x| Create two cases. One where x ≥ 0, and another where x < 0. Case 1: when x ≥ 0 If x ≥ 0, then the absolute value variable will remain positive, where the function will only apply to the positive x-axis, its domain. g(x) = x² - x Case 2: when x < 0 If x < 0, then the absolute value variable will become negative, where the function will only apply to the negative x-axis, its domain. h(x) = x² + x Graph both functions on the same Cartesian plane keeping in mind of their domains.
g(x) when simplified gives us two zeros: one at (0,0) and the other at (1,0). Since g(x)'s domain is only when x ≥ 0, it cannot pass further on after the zero at the origin, (0,0). h(x) when simplified gives us two zeros: one at (0,0) and the other at (-1,0). Since h(x)'s domain is only when x < 0, it cannot pass further on after the zero at the origin, (0,0).
Notice how, combining f(x) = x² - |x| and f(x) = x² + |x|, we get the graph of both functions if there were no absolute value variables involved.













