Sketch the graph of the function. f(x) = 3 + x if x < -1; x² if -1 ≤ x < 1; 2 - x if x ≥ 1.

Solution :

Given f(x) = 3 + x if x < -1

= x² if -1 ≤ x < 1

= 2 - x if x ≥ 1

Let f(x) = y

In order to plot a graph, we need to take sample values of x and plot

The lower limit should be less than -1, i.e. -2.

The upper limit should be greater than 1, i.e. 2.

The horizontal axis is the x-axis and the vertical axis is the y-axis.

Sketch the graph of the function. f(x) = 3 + x if x < -1; x² if -1 ≤ x < 1; 2 - x if x ≥ 1.

Summary:

The graph of the function. f(x) = 3 + x if x < -1; x² if -1 ≤ x < 1; 2 - x if x ≥ 1 is as shown.