How would you graph this piecewise function
f(x) = x^2 if lxl < or equal to 1
1 if lxl > 1
Thanks Very Much!
It looks like a table top with a dip in the middle
|x| <= 1 if -1<=x<=1
that's a small piece of the parabola, vertex at (0,0)
Now draw lines outward in both directions at y=1.
To graph the piecewise function f(x) = x^2 if |x| ≤ 1, and 1 if |x| > 1, you can follow these steps:
1. First, let's consider the function when |x| ≤ 1. This means that x can vary between -1 and 1, including those boundary values. For this interval, the function f(x) is given by f(x) = x^2.
2. Plot points on the graph for various values of x between -1 and 1. Choose a few x-values such as -1, -0.5, 0, 0.5, and 1, and calculate the corresponding y-values by substituting these x-values into the function f(x) = x^2. For example, when x = -1, f(-1) = (-1)^2 = 1; when x = 0, f(0) = (0)^2 = 0; when x = 1, f(1) = (1)^2 = 1. Plot these points on the graph.
3. Next, let's consider the function when |x| > 1. This means that x is any value greater than 1 or less than -1. For this interval, the function f(x) is constant and given by f(x) = 1.
4. Plot a horizontal line at y = 1, which represents the function f(x) = 1 for all x-values greater than 1 or less than -1.
5. Connect the plotted points and line segments to form the graph. The graph should resemble a "V" shape, with a parabolic curve within |x| ≤ 1, and a horizontal line at y = 1 beyond |x| > 1.
By following these steps, you can easily graph the piecewise function f(x) = x^2 if |x| ≤ 1, and 1 if |x| > 1.