Learning Resources

Using Graphs to Obtain Functional Notation

Answers to Self Test

For each of the graphs below:
(a)  Identify the type of function it represents (i.e. constant, linear, quadratic, etc.).
(b) Tell if the leading coefficient of the function is positive or negative.
(c) Indicate the number of real zeros and if they are distinct or identical.

1.  Quartic  ;  negative  ;  four distinct real zeros

2.   Linear  ;  negative  ;  one real zero

3.  Cubic  ;  negative  ;  three identical real zeros

4.  Quartic ;  positive ; two sets of two identical real zeros

5.  Cubic  ;  positive  ; one real zero

6.  Quadratic  ;  negative;  no real zeros

7.  f(x) = - x(x + 3)

8.  f(x) =  x(x+3)²  

9.  f(x) = (x + 3)

10. f(x) =  (x - 3)(x + 1)(x + 3)²