Graph the piecewise function:

Question

f(x) = { x^2 - 2 x > 0

{ x - 4 x ≤ 0

Answer 1

Because this is a piecewise function, you will need to graph this function in two parts. First, taking x^2 - 2 x > 0 you can plot points on the right side of the y axis. x^2 - 2 is a parabola that is shifted down by 2. Although not shown in the graph, there should be an open circle where 0 is for the function x^2 - 2 x > 0 because the inequality does not include 0. Next, we will focus on x - 4 x ≤ 0. Because x ≤ 0 is an inclusive inequality, we have a closed dot at x=0 for this function. Beyond that, you can graph the final function on the left side of the y axis!

I hope this helps and please feel free to reach out if you have more questions!