1. Grade Distribution 2nd 5th A 8 9 B 6 7 C 3 D 2 1 F 100+ Range 52-1023 D 2 1 F No
Shows
100+
Range
52-102
68-105
Avg
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3.1 - Functions

2. Pre-Calculus AB Pre-AP/Dual, Revised ©2015
Functions
Section 3.1
Pre-Calculus AB Pre-AP/Dual, Revised ©2015
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3.1 - Functions

3. Key Terms Relation is a pairing of 2 items (like (x, y))
Domain is the X –values in a relation. Also known as INDEPENDENT Variable
Range is the Y –values in a relation. Also known as DEPENDENT Variable
“Y depends on X.”
Function is a relation that for each domain element, there is only 1 range element. _X_ do not repeat.
To determine the domain,
Set the denominator EQUAL TO ZERO AND SOLVE. Those are your RESTRICTIONS
You cannot take the square root of a negative number, or the nth root, where n is negative. Put the radicand equation GREATER TO EQUAL to zero.
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3.1 - Functions

4. Vertical Line Test
Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point.
AKA: “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function
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3.1 - Functions

5. YES Example 1 Would this graph be a function? 1/16/2019 4:23 PM
3.1 - Functions

6. NO Example 2 Would this graph be a function? 1/16/2019 4:23 PM
3.1 - Functions

7. NO Discontinuous at zero Example 3 Would this graph be a function?
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3.1 - Functions

8. Example 4
Determine whether this function is defined as a function, y = x2 + 1?
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3.1 - Functions

9. Your Turn
Determine whether this function is defined as a function, y2 = x2 + 1?
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10. Example 5
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11. Example 6
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12. Example 7
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13. Your Turn
Determine whether the domain for the function, 𝒇 𝒙 = 𝒙 𝟐 (𝒙+𝟒)(𝒙−𝟏) in interval notation
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3.1 - Functions

14. Example 8 Given f (x) = x2 – 2x + 4, evaluate f (–5).
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15. Example 9 Given f (x) = x2 – 2x + 4, evaluate 𝒇 𝟐 1/16/2019 4:23 PM
3.1 - Functions

16. Example 10 Given f (x) = x2 – 2x + 4, evaluate f (x + 2).
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3.1 - Functions

17. Your Turn Given g (x) = x2 + 4, evaluate g(a + 1). 1/16/2019 4:23 PM
3.1 - Functions

18. Difference Quotient A. Difference Quotient: 𝒇 𝒙+𝒉 −𝒇(𝒙) 𝒉
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3.1 - Functions

19. Equation
Difference Quotient:
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20. Review
If f (x) = 2x + 3, solve for f(5) If f (x) = 2x + 3, solve for f(a) If f (x) = 2x + 3, solve for f(x + h)
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3.1 - Functions

21. Example 11
Given f(x) = 5x – 6, use the Difference Quotient to simplify
For every x, plug in a x
For every x, plug in a x + h
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3.1 - Functions

22. Example 12
Given f(x) = 2x2 – 1, use the Difference Quotient to simplify
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3.1 - Functions

23. Your Turn
Given f(x) = x2 – x + 2, use the Difference Quotient to simplify
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24. Assignment
Worksheet
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3.1 - Functions