Final answer:
To draw the graphs of f(x)=x⁴-6x² and g(x)=|x⁴-6x²|, we plot points on a coordinate plane and connect them. The graphs have the same shape, but g(x) includes a reflected part above the x-axis.
Step-by-step explanation:
To draw the graphs of the functions f(x)=x⁴-6x² and g(x)=|x⁴-6x²|, we can start by plotting points on a coordinate plane. We can choose values for x and calculate the corresponding values for f(x) and g(x). For example, if we choose x=-2, we get f(-2)=16-24= -8 and g(-2)= |-8|=8.
We repeat this process for other values of x and plot the points on the coordinate plane. To draw the graph of f(x)=x⁴-6x², we connect the points and get a curve similar to a parabola. To draw the graph of g(x)=|x⁴-6x²|, we connect the points and get a curve that is similar to the graph of f(x), but the part below the x-axis is reflected to be above the x-axis.
So, the graphs of f(x) and g(x) are related in that they have the same shape, but g(x) includes the reflected part above the x-axis.