Sketch the graph of the function. f(x) = 3 + x if x < -2; x² if -2 ≤ x < 2; 6 - x if x ≥ 2.

Solution:

Given: f(x) = 3 + x if x < -2
= x² if -2 ≤ x < 2
= 6 - x if x ≥ 2

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 -2, i.e. -3.

The upper limit should be greater than 2, i.e. 3.

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 < -2; x² if -2 ≤ x < 2; 6 - x if x ≥ 2.

Summary:

The graph of the function. f(x) = 3 + x if x < -2; x² if -2 ≤ x < 2; 6 - x if x ≥ 2 is as shown.