Key Concepts

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