2.1 Functions POWERPOINT

Alg 3(11) 14

Ch. 2.1- 2.3

I Vocabulary

a) Function: A 1-1 correspondence between 2 sets such that for each value in the domains set there is only 1 value in the range set. (No “x” repeat)

b) domain: “x” values

c) range: “y” values

II Functions ?

A. a) _____

b) y = 2x + 3 _____

c) y = |x| _____

d) _____

e) _____

f) _____

B. Function y = x - 11

Another way to write it f(x) = x - 11

Substitute numbers in for x f(23) = 12 when x = 23 then y = 12 (23,12)

f(-5) =

f(99) =

ex. If f(x) = |x| f(2) = ______Function? ______

C. Piecewise-defined functions

y = Function? ______

III Restrictions

1) Denominator 0 , ,

______

2) ,

IV Examples

f(-1) =

f(0) =

Find f (x + 2)

Functions

a) domain = ______range = ______

b) domain = ______

c) domain = ______

V Examples

1. If 2. If then find

find f(-3)

3. If f(x) =

a) find f(x + 2) b) find 3f( x)

3f(2)

Ch 2.2 Graphing POWERPOINT

I Def: An equation whose graph is a line is a linear equation.

Linear: Not Linear

II STANDARD FORM SLOPE INTERCEPT FORM

Ax +By = C y = mx + b

2x -3y = -2

write in standard form write in slope intercept form

y = x + 3 2x + 3y = 6

3x = 2y + ½ -5y + 2x = 10

III GRAPHING

x-intercept slope = m =

y-intercept

parallel lines

perpendicular lines

vertical lines

horizontal lines

IV EXAMPLES

1. Find the x and y intercepts for

a) 3x + y = 6 b) + y = 6

2. Find the slope for the lines through the following points:

a) (3,-5) (-3,-3) b) (-2,-3) (-1,1)

c) ( , ) ( ,)

d) graph a line with slope - ¼ through the point (2,3)

e) Find “t” if the line through ( -1,1) and (3,2) is parallel to the line through (0,6) and (-8, t).

f) Show the figure with the following vertices is a parallelogram.

A (1,2) B (4,-1) C (2,-2) D (-1,1)

g) Graph y = x + 6

h) Graph y = -2x + 1

i) Graph
2.3 Line Equations

I Slope – Intercept Form y = mx + b m = ______b = ______

To write the equation of a line you need the slope and a point on the line.

1. slope = 2, y – intercept = 4 (0,4) y = 2x + 4

2. slope = 2, point (2,3) a) sub in point and slope

b) find “b”

y = mx + b

3 = 2(2) + b

b = -1 y = 2x -1

3. 2 points a) find “m”

(1,2) (3,4) b) use one point with slope to find “b”

______

4. 2 intercepts a) write intercepts as points and find “m”

x-int = -2 b) use y – intercept for “b”

y-int = 3

______

5. point and a || line a) pull of slope from || line

(2,3) y = 2x + 3 b) use point to find “b”

( same as #2)

______

6. point and line a) pull of slope ( ______)

(2,3) y = 2x + 3 b) use pt. to find “b”

______

7. vertical line and point a) x = “x” value of point

(2,3) ______

8. horizontal line and point a) y = “y” value of point

(2,3) ______

Ex.

1. Write the equation of the line through (-1,3) and (3, 6)

2. Write the equation of the line through (-2, 6) and || to the line 3x – 2y = 4

Algebra Review Worksheet 2.1-2.3

(1) Find the domain of each of the following.

(a) (b)

(2) Given the function, find each of the following.

(a) (b)

(3) Sketch a graph of each of the following.

(a) y = -3x + 4 (b) 4x - 3y = 12

(4) Write the equation of the line which satisfies each of the following.

(a) Passes through (3 , 5) with slope -2

(b) Passes through (-7 , -4) with slope

(d) Passes through (3 , 5) and (-2 , 5)

(e) Passes through (3 , -6), and is parallel to the line 4x - 2y = 11

(f) Passes through (1 , 9), and is perpendicular to the line 5x + 3y = 2

(5) Triangle DABC has vertices A(2 , 1) , B(-1 , -5) , and C(6 , -1).

(a) Is DABC a right triangle?

(b) Write the equation of BC

(1) (a) (b)

(c) All Real Numbers (d)

(2) (a) -3 (b) -21

(4) (a) y = -2x + 11

(b)

(c)

(d) y = 5

(e) y = 2x - 12

(f)

(5) (a) yes

(b)

(c)

More Review of Slopes and Intercepts

slope =

Find the slope of the line between the two points given.

1. (3, -8) and (-5, 2) 2. (-10, -3) and (7,2)

3. (-7, -6) and (3, -6) 4. (8, 2) and (8, -1)

Graph.

5. (1, -3) and m = 3 6. (2, 1) and m = -3/4

Find the intercepts.

7. y = 7x + 5 8. y = -9x + 15

Parallel, Perpendicular, or Neither?

9. 2x + 3y = 4 10. 0.5x + 2y = 1

3x + 2y = 6 4x - y = 3

11. 6x - 9y = 4 12. y - 7 = 0

x- y = 11 3x = 5

Graph.

13. (0,0) and parallel to y =2x + 1 14. (1,4) and parallel to x + y = 1

15. (-4, 1) and perpendicular to a line whose slope is m = -5/3.

Answers for More Review Slopes and Intercepts

1) -4/5

2) 5/17

3) 0

4) undefined

5) 6)

7) (0,5), (-5/7, 0) 8) (0, 15) (5/3, 0)

9) neither 10) perpendicular 11) parallel 12) perpendicular

13) 14)

15)

2.1-2.3 Additional Review

Find each value if f(x)=.

6. f(3) 7. f(-4)

8. f(1/2) 9. f(-2)

10. f(0) 11. f(m-2)

Write each equation in standard form

12. 13. 3y - 5 = 0

Determine the slope of the line passing through each pair of points.

14) (3, 4) and (-2, 1) 15) (6, 0) and (6, 3)

Find the slope-intercept form of each equation.

16) 4x + 7y = 12 17) 3x - 2y = 4

Find the x- and y-intercepts

18) 5x - 4y = 8 19) 3x - y = -11

20) 21) 3y = 7

Write an equation for the line that satifies each of the given conditions in slope-intercept form. Graph the lines on a separate sheet of graph paper. Label at least two points!

22) slope= -5, passes through (-3, -8) 23) slope= 4/5, passes through (10,-3)

24) passes through (4,3) and (7,-2) 25) passes through (3,11) and (-6,5)

26) passes through (7,2) and (3,-5) 27) x-intercept = 3, y-intercept = 2

28) x-intercept = -5, y-intercept=-5 29) vertical line passing through (1,5)

Answers for 2.1-2.3 Review

6) 7) f(-4) = -5/2

8) f(1/2) = 2 9) undef

10) f(0) = 5/2 11) f(m-2) = 5/m

12) 28x + 8y = 21 13) 3y = 5

14) 3/5 15) undef

16) y = -4/7x + 12/7 17) y = 3/2x- 2

18) (0,-2), (8/5, 0) 19) (0,11) (-11/3, 0)

20) (0, 7/4), (3/2, 0) 21) no x-int, (0, 7/3)

22) y = -5x-23 23) y = 4/5 x -11

24) y = -5/3 x + 29/5 25) y = 2/3 x + 9

26) y = 7/4 x – 41/4 27) y = -2/3 x + 2

28) y = -x – 5 29) x = 1