8.1 Relations and Functions (Page 404) Essential Question: What
is the difference between a function and a relation?
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8.1 cont. Relation: A set of ordered pairs Note: { } are the
symbol for "set" Examples: 1. { (0,1), (55,22), (3,-50) } 2. { (0,
1), (5, 2), (-3, 9) } 3. { (-1,7), (1, 7), (33, 7), (32, 7) } Any
group of numbers is a relation as long as the numbers come in
pairs
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8.1 cont.
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Domain First coordinates of the relation Range Second
coordinates of the relation Tip: Alphabetically x comes before y,
and domain comes before range DOMAIN RANGE
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8.1 cont.
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Mapping diagrams: Shows whether a relation is a function Steps:
1. List domain values and range values in order 2. Draw arrows from
domain values to corresponding range values 2 range values for
domain value 1 NOT a function 1 range value for each domain value
IS a function 1 range value for each domain value IS a
function
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8.1 cont. No, there are two range values for the domain value
2
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8.1 cont. Functions can model everyday situations when one
quantity depends on another One quantity is a function of the other
Example 3: Is the time needed to cook a turkey a function of the
weight of the turkey? Explain. The time the turkey cooks (range
value) is determined by the weight of the turkey (domain value).
This relation is a function!
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8.1 cont. Vertical-Line Test Visual way of telling whether a
relation is a function If you can find a vertical line that passes
through two points on the graph, then the relation is NOT a
function
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8.1 cont. Example 4: Graph the relation shown in the following
table:
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8.1 - Closure What is the difference between a function and a
relation? Any set of ordered pairs is a relation A function is a
relation with the restriction that no two of its ordered pairs have
the same first coordinate
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8.1 - Homework Page 407-408, 2-28 even
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Bell Ringer
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8.2 Equations With Two Variables (Page 409) Essential
Questions: What is the solution of an equation with two variables?
How can you graph an equation that has two variables?
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8.2 cont.
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Linear Equations: Any equation whose graph is a line ALL
equations in this lesson are linear equations Solutions can be
shown in a table or graph
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8.2 cont. Example 2: For the following equation, make a table
of values to show solutions. Then, graph your results.
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8.2 cont. Vertical Line Test Every x-value has exactly 1
y-value Therefore, this relation IS a function Linear equations are
functions unless its graph is a vertical line NOT A FUNCTION!!
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8.2 cont.
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8.2 - Closure What is the solution of an equation with two
variables? Any ordered pair that makes the equation a true
statement How can you graph an equation that has two variables?
Make a table of values to show ordered-pair solutions of the
equation Graph the ordered pairs, then draw a line through the
points
Slide 25
8.2 - Homework Page 412, 2-36 even
Slide 26
Bell Ringer
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8.3 Slope and y-intercept (Page 415) Essential Question: What
is an easier way to graph linear equations?
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8.3 cont. Slope: Ratio that describes the tilt of a line To
calculate slope, use the following ratio:
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8.3 cont. POSITIVE SLOPE NEGATIVE SLOPE ZERO SLOPE UNDEFINED
SLOPE
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8.3 cont.
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Horizontal and Vertical Lines:
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8.3 cont.
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8.3 - Closure What is an easier way to graph linear equations?
USE SLOPE-INTERCEPT FORM!!
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8.3 - Homework Page 418-419, 2-18 even, 24-38 even
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Bell Ringer y-intercept slope
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8.4 Writing Rules for Linear Functions (Page 422) Essential
Question: How can we use tables and graph to write a function
rule?
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8.4 cont.
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Writing Function Rules From Tables or Graphs Look for a
pattern! May need to add, subtract, multiply, divide, or use a
power OR a combination of these operations
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8.4 cont. Example 2: Write a rule for each of the following
linear function tables:
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8.4 cont. Example 3: Write a rule for the linear function
graphed below:
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8.4 - Closure How can we use tables and graphs to write a
function rule? Look for a pattern using a combination of addition,
subtraction, multiplication, division, and powers Use slope and
y-intercept to write a linear function
Slide 45
8.4 - Homework Page 424-425, 2-22 even
Slide 46
Bell Ringer Plot your given point on the coordinate plane:
Slide 47
8.5 Scatter Plots (Page 427) Essential Question: How can we
make scatter plots and use them to find a trend?
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8.5 cont. Scatter Plots: Shows a relationship between two sets
of data
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8.5 cont. Example 1: Make a scatter plot for the data in the
table below: Age (in years) Value (in thousands)
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8.5 cont. Example 2: Make a scatter plot for the data
below:
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8.5 cont. Trends:
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8.5 cont. Trend Line: Shows relationship between data sets
Allows us to make predictions about data values Possible to have no
trend line
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Example 3: Use the following scatter plot to predict the height
of a tree that has a circumference of 175 in: 88 ft
Slide 54
8.5 - Closure How can we make scatter plots and use them to
find a trend? 1. Plot ordered pairs 2. Draw a trend line (positive,
negative, or no trend) 3. Predict values
