Question

Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice.

Answer 1

1. Let the function be

f(x)=

5 for x<2
3 for x=2
x for x>2

2.

In the interval (-∞, 2) the function is f(x)=5. So for any x in (-∞, 2), f(x)=5, which makes the collection of all the points (x,f(x)) a horizontal line passing through 5.

for x=2, f(x)=f(2)=3. So we have the point (2, 3)

in (2, ∞) the function is f(x)=x. for example, f(4)=4, f(7)=7... the collection of all these points is a straight line with an inclination of 45°.

3. draw the graph (check the picture)