Key Concepts

• When a graph of [latex]y=f(x)[/latex] is above the [latex]x[/latex]-axis, [latex]f(x)>0[/latex].
  So, the solution of the inequality [latex]f(x)>0[/latex] is the interval of [latex]x[/latex] where the graph of [latex]y=f(x)[/latex] is above the [latex]x[/latex]-axis.
• When a graph of [latex]y=f(x)[/latex] is on the [latex]x[/latex]-axis, [latex]f(x)=0[/latex].
  So, the solution of the equation [latex]f(x)=0[/latex] is the [latex]x[/latex] values of its [latex]x[/latex]-intercepts.
• When a graph of [latex]y=f(x)[/latex] is below the [latex]x[/latex]-axis, [latex]f(x)<0[/latex]. So, the solution of the inequality [latex]f(x)<0[/latex] is the interval of [latex]x[/latex] where the graph of [latex]y=f(x)[/latex] is below the [latex]x[/latex]-axis. Also, the solution of the inequality [latex]f(x) \geq g(x)[/latex] is the interval of [latex]x[/latex] where the graph of [latex]y=f(x)[/latex] is above or intersecting the graph of [latex]y=g(x)[/latex].
• When a graph of [latex]y=f(x)[/latex] is above the graph of [latex]y=g(x)[/latex], [latex]f(x)>g(x)[/latex].
  So, the solution of the inequality [latex]f(x)>g(x)[/latex] is the interval of [latex]x[/latex] where the graph of [latex]y=f(x)[/latex] is above the graph of [latex]y=g(x)[/latex].
• When a graph of [latex]y=f(x)[/latex] is intersecting the graph of [latex]y=g(x)[/latex], [latex]f(x)=g(x)[/latex].
  So, the solution of the equation [latex]f(x)=g(x)[/latex] is the [latex]x[/latex] values of the intersecting points of [latex]y=f(x)[/latex] and [latex]y=g(x)[/latex].
• When a graph of [latex]y=f(x)[/latex] is below the graph of [latex]y=g(x)[/latex], [latex]f(x)