2017 Honors Precalc Chapter 1 Notes Name __________________________________ Period______ Date______

A# S Date Pg Assignments

1 1.1 8/29 11 1, 2, 3, 4B, 6,10-14 even, 18 (20, 22 equations only), 36, 44, 46, 48-50, 54, 56, 58, 61

2 1.2 8/30 24 2, 7, 9,13-23 odd [27, 35-39 odd (A & C)] 45, 49, 51

3 1.2 8/31 26 53-61, 87, 89, 90, 93, 94, 99-103 odd, 71, 75 (hint: think slope and area)

4 1.3 9/1 38 1-4, 5-9 odd no GC, 13, 29, 49, 51, 53, 61 no GC, 69, 71, 72, 85 no GC, 93-100

5 1.4 9/5 48 1-6, 11, 13,15-20, 27-32, 43, 47, 55, 59, 61, 65, 67, 71-74

    WS 1.3 Piecewise and Greatest Integer Function WS

6 1.5 9/6 58 5, 9, 12, 13, 21-25odd, 36, 41-47 odd, 49a, 61, 63, 78(a,b)

7 1.6 9/7 699a, 11a, 17, 20-24 all, 29-34, [36, 41, 43 no GC], 49, 53, 57, 69, 79, 83, 87, 93-103odd, 111, 113

8 R 9/8 83 19, 33, 41-49, 51, 69-73, 76, 121, 133, 134 + Additional Modeling Worksheet

    9/11   Chapter 1 Test

    9/12   FRQ

1.1 Equations of Lines

Finding Slope Given a Line:

Given two points:

Find Slope and Y-intercept

Given an equation in standard form:

1

Find the Equation of a Line

Given a slope and a point:

Given two points:

Given a parallel line and a point:

Given a perpendicular line and a point:

1.2 Functions

2

Functions can be expressed the following ways:

1. Mapping 4. Points 5. Equations

2. Table 3. Graphs 6. Written Form

Test For a Function

Look For Is a Function Is Not a Function

Points/Tables

x listed twice

6. 7.

Mapping

Domain value has two arrows

8.

9.

Graph

Vertical Line Test

10. 11.

Equation

Solve for y

12. 13.

3

Function Notation

Let f (x)=−2x2+4 x. Find the following.

14.f (−4 ) 15.f (h) 16.f (x+h)

Let . Find the following.

17.f (4 ) 18.f (1) 19.f (−6)

4

Difference Quotient

A. B.

19. Let f (x)=−2x2+4 x. Find the difference quotient.

a. f (x+h) b. −f (x)

c. Find the difference quotient.

5

20. Let f (x)= 3x−2 . Find the difference quotient.

a. f (x+h) b. −f (x)

c. Get a common denominator in the numerator.

d. Put it all together and find the difference quotient.

Basic Parent Graphs: The domain refers to the domain values that are used for the parent function.

21. Linear Function domain -2, -1, 0, 1, 2 22. Constant Function f (x)=c domain -2, -1, 0, 1, 2

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23. Quadratic Function domain -2, -1, 0, 1, 2 24. Cubic Function domain -2, -1, 0, 1, 2

25. Square root domain 0, 1, 4 26. Cube Root domain -8, -1, 0, 1, 8

27. Absolute Value domain -2, -1, 0, 1, 228. Rational Function domain -2, -1, 0, 1, 2

7

29. Greatest Integer Function

domain -2, -1, 0, 1, 2

30. Half Circle

31. Let f (x)= −7x+2 . Find the difference quotient.

8

Find the domain of the following functions in interval notation.

32. 33.

34. 35.

36. 37.

Application Problems

“Write f as a function of x”

-means-

f(x)= equation with x in it.

38.

9

39.

Review: Find the domain of the following functions in interval notation.

10

A. B. C.

D. E.

F.

1.3 Graphs of Functions

Basic Parent Graphs: The domain refers to the domain values that are used for the parent function.

1. Cube Root domain -8, -1, 0, 1, 82. Rational Function domain -2, -1, 0, 1, 2

Domain Range Domain Range

3. Greatest Integer Function

domain -2, -1, 0, 1, 2

4. Half Circle

11

Domain Range Domain Range

5. 6. Half Circle

Domain Range Domain Range

7. domain -2, -1, 0, 1, 28. domain -1, -0.5, 0, 0.5, 1

Domain Range Domain Range

Even and Odd Functions (not degree, this is about symmetry)

12

Even Odd

f(-x )= f(x) f(-x )= - f(x)

9. 11.

10. Prove if f has even, odd, or neither symmetry. 12. Prove if f has even, odd, or neither symmetry.

13

1.3 Piecewise Functions13. What is a piecewise function? 14. Write a piecewise function.

Graphing Piecewise Function

1) Label parent graphs

2) Find endpoints for each functions (holes and dots)

3) Connect the points with the correct parent graph.

15. 16. Graph the following and find:

14

1.4 Shifting, Reflection, and Stretching Graphs

Let f be the line segment that connects the points (0, 1) and (2, 3). Graph the following:

7. f(x) + k shift up k units. 8. f(x) – k shift down k units. 9. f(x + h) shift left h units.

15

10. f(x-h) shift right h units. 11. –f(x) is f(x) reflected about the x-axis

12. f(–x) is the mirror of f(x) reflected about the y-axis

13. - 4

Shift right 2 and down 4

14. +2

Reflect over x-axis and up 2

15.

Factor -1 and reflect over the y-axis

then flip over x axis

left 1

16. Multi the y values by 2 17. Multi the y values by and flip over x axis

18. Multiply the x values by 1/2

16

19.

Multi the y values by 2

Inside the ( )’s factor -1

reflect over the y-axis (multiply the y values by -2)

then flip over x axis

left 1 and up 3

Perform the following transformations.

17

A) B)

C) D)

E) F)

18

G) H)

I) f (x)=[−x+1]+2

J)

19

1.5 Combination of Functions

a. What is the domain of . b. What is the domain of .

c. What is the domain of . d. What is the domain of .

1. Given and find the following:

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a.

b.

c. Find the domain from part a.

d. Find the domain from part b.

21

Compositions of Functions

2. Given and find the following:

a. b.

c. Find the domain for part a. and

22

1.6 Inverse Functions

A. Given a function, how do you know the function has an inverse function? B. Prove is one-to-one.

23

C. Does have an inverse function? D. Does have an inverse function?

E. Does and have an inverse function?

24

F. What must you show to prove two functions are inverse functions of each other?

G. Graph the inverse function if it exists.

1. Let . Prove that f and g are inverse functions.

a. b.

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2. Let . Complete the following.

a. Does f have an inverse? b. If f has an inverse find it. Remember to write the

notation .

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c. What must you show to prove f and are inverse functions?

Prove that f and are inverse functions.

d. e.

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f. What is the domain of f?g. What is the domain of ?

h. What is the range of f? i. What is the range of ?

3. Find the inverse function of f if it exists. .

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4. Let and find the following.

a. Find f inverse. b. Find g inverse.

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c. d.

30