Understanding Engineering Mathematics

y

− 4 − 3 − 2 − 10 1 2 3 4 x

4

3

2

1

− 1

− 2

− 3

− 4

(1,3)

(0,1)

y = 2 x + 1

Figure 3.1The graph ofy= 2 x+1.

Like the linear function all the common functions have characteristic graphs. Some are
given in the reinforcement exercises and others you will meet as they arise in the book.
One important point to note is that here we are talking aboutplottingrather thansketching
a graph (see Chapter 10).

Solution to review question 3.1.2

Evaluating the functiony=x^2 − 2 x−3 at the given values ofxyields

the coordinates:

x − 2 − 101234

y 50 − 3 − 4 − 305

The graph drawn through these points is shown in Figure 3.2. Remember

to label your axes!

This is a quadratic function. It crosses thex-axis wherex^2 − 2 x− 3 =0.

We can solve this quadratic equation by factorisation:

x^2 − 2 x− 3 =(x− 3 )(x+ 1 )= 0