Unit 1.3

1. 1.3
Twelve Basic
Functions
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2. What you’ll learn about
 What Graphs can Tell Us
 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.
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3. The Identity Function
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4. The Squaring Function
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5. The Cubing Function
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6. The Reciprocal Function
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7. The Square Root Function
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8. The Exponential Function
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9. The Natural Logarithm Function
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10. The Sine Function
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11. The Cosine Function
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12. The Absolute Value Function
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13. The Greatest Integer Function
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14. The Logistic Function
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15. Example Looking for Domains
One of the functions has domain the set of all reals
except 0.
Which function is it?
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16. Solution
One of the functions has domain the set of all reals
except 0.
Which function is it?
The function y  1/ x has a vertical asymptote at x  0.
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17. Example Analyzing a Function
Graphically
Graph the function y  x2  1.
Then answer the following questions.
(a) On what interval is the function increasing? decreasing?
(b) Is the function even, odd, or neither?
(c) Does the function have any extrema?
(d) How does the graph relate to the graph of the basic
function y  x2 ?
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18. Solution
Graph the function y  x2  1.
(a) Increasing on ,0 and decreasing 0,
(b) Symmetric with respect to the y-axis, but not the x-axis
so the function even.
(c) Maximum value of  1 at x  0
(d) The graph is the grpah of y  x2 reflected over the
x-axis and translated 1 unit down.
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19. Quick Review
Evaluate the expressions without using a calculator.
1. 43.21
2.   4
3. ln 1
4. e0
5. 4 4  4
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20. Quick Review Solutions
Evaluate the expressions without using a calculator.
1. 43.21  43.21
2.   4  4  
3. ln 1  0
4. e0  1
5. 4 4  4
 4
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