bell ringer. linear functions and graphing 8.1 – relations and functions (page 404) essential...
TRANSCRIPT
- Slide 1
- Bell Ringer
- Slide 2
- Linear Functions and Graphing
- Slide 3
- 8.1 Relations and Functions (Page 404) Essential Question: What is the difference between a function and a relation?
- Slide 4
- 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
- Slide 5
- 8.1 cont.
- Slide 6
- 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
- Slide 7
- 8.1 cont.
- Slide 8
- 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
- Slide 9
- 8.1 cont. No, there are two range values for the domain value 2
- Slide 10
- 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!
- Slide 11
- 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
- Slide 12
- 8.1 cont. Example 4: Graph the relation shown in the following table:
- Slide 13
- 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
- Slide 14
- 8.1 - Homework Page 407-408, 2-28 even
- Slide 15
- Bell Ringer
- Slide 16
- 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?
- Slide 17
- 8.2 cont.
- Slide 18
- Slide 19
- 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
- Slide 20
- 8.2 cont. Example 2: For the following equation, make a table of values to show solutions. Then, graph your results.
- Slide 21
- 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!!
- Slide 22
- 8.2 cont.
- Slide 23
- Slide 24
- 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
- Slide 27
- 8.3 Slope and y-intercept (Page 415) Essential Question: What is an easier way to graph linear equations?
- Slide 28
- 8.3 cont. Slope: Ratio that describes the tilt of a line To calculate slope, use the following ratio:
- Slide 29
- 8.3 cont. POSITIVE SLOPE NEGATIVE SLOPE ZERO SLOPE UNDEFINED SLOPE
- Slide 30
- 8.3 cont.
- Slide 31
- Horizontal and Vertical Lines:
- Slide 32
- 8.3 cont.
- Slide 33
- Slide 34
- Slide 35
- 8.3 - Closure What is an easier way to graph linear equations? USE SLOPE-INTERCEPT FORM!!
- Slide 36
- 8.3 - Homework Page 418-419, 2-18 even, 24-38 even
- Slide 37
- Bell Ringer y-intercept slope
- Slide 38
- 8.4 Writing Rules for Linear Functions (Page 422) Essential Question: How can we use tables and graph to write a function rule?
- Slide 39
- 8.4 cont.
- Slide 40
- Slide 41
- 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
- Slide 42
- 8.4 cont. Example 2: Write a rule for each of the following linear function tables:
- Slide 43
- 8.4 cont. Example 3: Write a rule for the linear function graphed below:
- Slide 44
- 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?
- Slide 48
- 8.5 cont. Scatter Plots: Shows a relationship between two sets of data
- Slide 49
- 8.5 cont. Example 1: Make a scatter plot for the data in the table below: Age (in years) Value (in thousands)
- Slide 50
- 8.5 cont. Example 2: Make a scatter plot for the data below:
- Slide 51
- 8.5 cont. Trends:
- Slide 52
- 8.5 cont. Trend Line: Shows relationship between data sets Allows us to make predictions about data values Possible to have no trend line
- Slide 53
- 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
- Slide 55
- 8.5 - Homework P 430-432; 2-30 even