1. Twelve Basic Functions
1.3
Twelve Basic Functions

2. What you’ll learn about
What Graphs Can Tell You
Twelve Basic Functions
Analyzing Functions Graphically
… and why
As you continue to study mathematics, you will find
that the twelve basic functions presented here will come
up again and again. By knowing their basic properties,
you will recognize them when you see them.

3. The Identity Function Domain: Range: Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

4. The Quadratic Function
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

5. The Cubic Function Domain: Range: Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

6. The Reciprocal Function
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

7. The Square Root Function
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

8. The Absolute Value Function
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

9. The Exponential Function
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

10. The Natural Logarithm Function
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

11. The Greatest Integer Function
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

12. The Logistic Function Domain: Range: Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

13. The Sine Function Domain: Range: Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

14. The Cosine Function Domain: Range: Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):

15. Piecewise Function Example
Domain:
Range:
Asymptotes (if any):
Symmetry (if any):
x-intercepts (Roots):
y-intercepts (if any):
Continuous (y/n):
Periodic (y/n):
Bounded (y/n):
𝑦= 𝑥+4 , 𝑥 <−1 𝑥 2 , −1≤ 𝑥 ≤2 4, 𝑥 >2

16. Homework
Page 113
#1-24

17. Functions

18. Functions (cont’d)