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UNIT 21.7, 4.8 Introduction to Functions
HW: 1.7 12 – 24 m3, 264.8 11 – 22
function: A rule that relates two numbers called the input and output. For every input there is exactly one output.
Examples
1.7, 4.8Introduction to FunctionsDefinitions
input: a number entered into a function. (DOMAIN)
output: the result of entering a number into a function. (RANGE)
domain: the collection of all input values for a function (the x-values)
range: the collection of all output values for a function (the y-values and )
1.7, 4.8 Introduction to Functions
Make an input-output table for the function below. Use 1, 2, 3, 4, and 5 as the domain:
Domain Range
Input Output
1 5
2
3
4
5
1.7, 4.8 Introduction to Functions
Make an input-output table for the function below. Use 1, 2, 3, 4, and 5 as the domain:
Domain Range
Input Output
1 0.5
2
3
4
5
1.7, 4.8 Introduction to Functions
Solutiona. Is a function. For every ONE input there is a unique OUTPUT. Domain: Range:Solution“b” Is a NOT a function. The input {1} has two different outputs {5, 7}.
1.7, 4.8 Introduction to FunctionsPractice
Decide whether the graph represents y as a function of x. If yes, then state the domain and range.
Unit 24.3 Quick graph (x, y intercepts)
4.6 Quick graph (slope-intercept)
Homework (due Monday)• 4.3 15 – 54 m3 no 33• 4.6 24 – 45 m3• Use any method to graph. Ignore the
directions.• Two lines per coordinate plane.
4.3 Quick graph (x, y intercepts)4.6 Quick graph (slope-intercept)
• Which method to use depends on how the problem looks when given to you.
• Use x, y intercepts
• Use slope-intercept
Method #2Quick graph using x, y intercepts
• Make an x, y T-table• Make x = 0 and solve for y. (y – intercept)• Make y = 0 and solve for x. (x – intercept)• Plot the two intercepts and draw the line.
4.6 Graphing lines using the slope and y-intercept
• Slope intercept Form
Slope y – intercept – starting point on the Y- axis
Directions to the next point
y bmx
m
UNIT 2 4.4 The slope of a line
5.1 writing a linear equation.
𝑚=𝑦2− 𝑦1
𝑥2− 𝑥1
Homework4.4 21 – 41 odd5.1 12 – 22 even write all equations in Slope - intercept form and Standard form
Slope Slope -intercept Standard𝑦=𝑚𝑥+𝑏 𝐴𝑥+𝐵𝑦=𝐶
x
y
run change in x
The slope m of the nonvertical linepassing through the points (x1, y1) and (x2, y2) is
Read y1 as “y sub one”Read x1 as “x sub one”
m = =
(x1, y1)
(x1, y1)
(x2, y2)
(x2, y2)
y2 - y1
(y2 - y1 )(y2 - y1 )
x2 - x1
(x2 - x1 )(x2 - x1 )
FINDING THE SLOPE OF A L INE
(x2, y2)(x1, y1)
rise change in y =
Examples
Find the slope of the line passing through the given points.
𝑚=𝑦2− 𝑦1
𝑥2− 𝑥1
𝑚=10−41−0
x, y x, y
𝑚=61
𝑚=6
𝑚=𝑦2− 𝑦1
𝑥2− 𝑥1
𝑚=−7−9−6−2
𝑚=−16−8
𝑚=2
5.1 Writing linear equationsSlope intercept form
Standard formare integers
• Given the slope and the y – intercept , simply substitute slope – intercept form.
• Rewrite the equation into Standard form.
5.1 writing linear equations given slope and y - intercept
• E.g.• Write in slope - intercept form 1)m = 4 and b = 1
slope – intercept formstandard form
You will have TWO answers.
5.1
2) Slope = and the y – intercept = -4
𝑦=𝑚𝑥+𝑏𝑦=−
25𝑥−4 slope – intercept form
25𝑥+𝑦=−4
2 𝑥+5 𝑦=−20 standard form
Unit 25.2, 5.3 writing linear equations
Homework5.2 12 – 33 m35.3 from power point Write all equations in slope – intercept form and standard form and
5.3 homeworkGive your self 5 spaces per problem
1. (3 ,5 ) ,(4 ,10)
7. (4 ,−7 ) ,(3 ,−7)
2 . (4 ,2 ) , (6 ,3) 6. (8 ,−5 ) , (6 ,−4)5. (3 ,5 ) ,(0 ,1)
3 . (−2 ,2 ) ,(0 ,−2)
4. ( 8 ,3 ) ,(3 ,13) 8. (1 ,−3 ) ,(−2 ,−1)
Write a linear equation in slope – intercept form and standard form.
5.2 writing linear equations given slope and a point
Point – slope form m = the slope given
is the point given
5.2 writing linear equations given slope and a point
1) m = 2, ( 5, 15)
2) m = 3, ( 2, -6)
3) m = , ( -8, 4)
4) m = -2, ( -3, 8)
5) m = , ( 9, -1) 1
2
2
3
5.3 writing linear equations given two points.
• Step 1– Find slope m =
• Step 2 – Substitute m and one of the given points into
point – slope form
2 1
2 1
y y
x x
5.3 writing linear equations given two points.
1) (5, 8), (7, 12)
2) (2, 4), (3, 7)
3) (-1, 8), (2, 2)
Cw 5.2Write an equation of a line.
1) m = 3, (1, 8)
2) m = -1, (2, 4)
3) m = 4, (-1, 3)
4) m = -5, (7, -2)
5) m = , (4, 7)
6) m = -4, (-3, -7)
7) m = 1, (0, -6)
8) m = , (3, -5)
1
2
1
3
3 5y x
6y x
4 7y x
5 33y x
15
2y x
4 19y x
6y x
16
3y x
Hw 5.2, 5.3 Power point Write an equation of a line.
9) (1,6),(4,12)
10) (4,2),(5,5)
11) (-2,4),(1,1)
12) (0,10),(4,2)
13) ( 2,9), (0,13)
14) (8,5),(3,0)
15) (-2,-5), (-4,0)
16) (10,9), (8,9)
2 4
3 10
2
2 10
y x
y x
y x
y x
2 13
3
510
2
9
y x
y x
y
y