Sketch the graph of the function. f(x) = 4 + x if x < -2; x² if -2 ≤ x < 2; 6 - x if x ≥ 2.

Solution :

Given: f(x) = 4 + 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 x-axis and the vertical axis is y-axis

Sketch the graph of the function. f(x) = 4 + x if x < -2; x² if -2 ≤ x < 2; 6 - x if x ≥ 2.

Summary:

The graph of the function. f(x) = 4 + x if x < -2; x² if -2 ≤ x < 2; 6 - x if x ≥ 2 is as shown.