We want to graph the given function in a graphing calculator. To do this, we need to first push Y= and type the equation in the first row. Then we push GRAPH to draw it.
Examining the graph, we can see that there are no values of x that the function cannot take.Therefore, the domain is all real numbers.
Domain: All real numbersTo find the range, we have to determine how far the function dips below the x-axis. We can see that its lowest value occurs along its line of symmetry. This line coincides with the second degree equation's line of symmetry that we see underneath the cube root.
f(x)=sqrt(3x^2-x)
The line of symmetry for a second degree equation can be determined with the following formula.
x=- b/2a
In this formula, a is the coefficient to x^2 and b is the coefficient to x. In our equation, we can identify these values as a=3 and b=-1.
