Algebra Chapter 4: FUNCTIONS Name: Teacher: Pd:
Table of Contents Day1: Chapter 4-1: Relations SWBAT: (1) Identify the domain and range of relations and functions (2) Match simple graphs with situations Pgs. #1-7 Hw pgs. #7-9 Day2: Chapter 4-2: FUNCTIONS SWBAT: Determine if a relation is a function, by examining ordered pairs and inspecting graphs of relations Pgs. #10-14 Hw pgs.15-16 Day3: Chapter 4-4: Graphing Linear/Exponential and Quadratic Functions SWBAT: (1) Graph linear, exponential and quadratic functions (2) Determine if a point is a solution of a line (3) Translate Quadratic Functions Pgs. #17-23 Hw pgs. 23-25 Day4: Chapter 4-4: Graphing Exponential and Quadratic Functions SWBAT: (1) Graph Exponential and Quadratic Functions (2) Translate Exponential and Quadratic Functions Pgs. #26 32 Hw pgs. # 33-35 Day 5: Chapter 4 REVIEW Hw pgs. #36-43
Chapter 4 1 Relations and Functions (Day 1) SWBAT: (1) Match simple graphs with situations (2) Identify the domain and range of relations and functions Warm Up: A set of ordered pairs is called a. A relation can be depicted in several different ways. An equation can represent a relation as well as,, and. 1
Using the mapping to the right, right the ordered pairs that represent this relation. (, ), (, ), (, ), (, ), (, ). 2
Example 1: Express the relation {( 4, 1), ( 1, 2), (1, 4), (2, 3), (4, 3)} as a table, a graph, and a mapping. Then, state the domain and range of the relation. Practice Problems: a) Express the relation {( 2, 1), ( 1, 0), (1, 2), (2, 4), (4, 3)} as a table, a graph, and a mapping. Then, state the domain and range of the relation. 3
b) Express the relation {( 3, 3), ( 1, 1), (0, 2), (2, 3), (2, 3)} as a table, a graph, and a mapping. Then, state the domain and range of the relation. 4
Example 2: PRACTICE PROBLEMS: YOU TRY! 5
4. Sketch the graph of the situation below. Challenge Problem: SUMMARY 6
Exit Ticket 7
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Chapter 4 2 FUNCTIONS (Day 2) SWBAT: Determine if a relation is a function, by examining ordered pairs and inspecting graphs of relations Warm Up: Definition A function is a relation in which each element of the domain is paired with exactly one element of the range. Vertical Line Test: If each vertical line passes through no more than one point of the graph of a relation, then the relation is a function. 10
Example 1: Determining if a Relation is a Function Practice: Determining if a Relation is a Function Example 2: Determining if a Relation is a Function 11
Practice: Determining if a Relation is a Function Example 3: Determining if a Relation is a Function (Vertical Line Test) Practice: Determining if a Relation is a Function (Vertical Line Test) 12
Example 4: Determining if a Relation is a Function J) K) Practice: Determining if a Relation is a Function 16) 17) 18) Challenge Problem: 13
Summary Exit Ticket: 14
Homework 4-2 Directions: Tell whether the relation is a function. Explain. 15
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SWBAT: Graph Linear functions given a limited domain Warm Up: Chapter 4 4 Graphing Linear Functions (Day 3) 17
X Y 18
y 4x 3 The point whose coordinates are (4,13) lies on the line. When y = -15, then x = Practice a) y = x + 4 (1,5) b) y = x + 3 (-2, 1) c) y = x 2 (6, 4) d) y = x 5 (3, 2) Answer the following questions without drawing a graph. e) If (k, 4) lies on the graph of y = x + 1, find k. f) If (k, -3) lies on the graph of x + y = -9, find k. g) If (5, k) lies on the graph of y = -x + 6, find k. h) If (-2, k) lies on the graph of y x = 5, find k. 19
Exponential Functions An exponential function is of the form y = a where a is nonzero, b 0, b 1, and x is a real number. Use the table of values below to graph the exponential function. x y The graph of an exponential function will never the x-axis. 20
Quadratic Functions A quadratic function is an equation in the form y = ax2 + bx + c, where a, b, and c are real numbers and a 0. The shape of a quadratic function is a, a smooth and symmetric U- shape. Investigate and generalize how changing the coefficients of a function affects its graph Example 5: Graph y = -x2, y = x2, and y = 3x2 on the graph below. x y=-x2 y= x2 y=3x2-2 -1 0 1 2 Observations from above: (1)When y= (2) When y= the graph is than (3) When y= the graph opens. the graph is than y= y= (which means its reflected over the axis) Example 6: Graph y = x2 + 2, and y = x2-3 on the graph below. x y=x2 + 2 y=x2-3 -2-1 0 1 2 Observations from above: (1) When y= the graph is shifted. (2) When y= the graph is shifted. 21
Challenge SUMMARY 22
Exit Ticket Day 3 - HW 1) 2) 23
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1. 2. Explain below. Explain below. 3. 4. Explain below. Explain below. 25
Chapter 4 4 GRAPHING ABSOLUTE VALUE FUNCTIONS (Day 4) SWBAT: Graph Absolute Value functions Warm Up: VERTEX The vertex of the absolute value function is the point where the function changes direction. Which coordinates are the turning points (vertex) of the graph above? (, ) 26
Exercise #2: Graph the following functions using a graphing calculator. y = y = SUMMARY When y= When y= the graph is shifted the graph is shifted 27
Exercise #3: Consider the function: y and y (a) Using your graphing calculator to generate an xy-table, graph this function on the given grid. y y SUMMARY Compare the graphs for problem 4. Make a conjecture about functions that come in the form: y=. When y= When y= the graph is shifted the graph is shifted 28
A translation is a shift of a graph vertically, horizontally, or both. The resulting graph is the same size and shape as the original but is in a different position in the plane. Practice: Writing equations of an absolute value finction from its graph. Write an equation for each translation of y= shown below. a) b) c) d) e) f) 29
Vertical and Horizontal Translations Identify the vertex and graph each. g) y= h) y = Vertex: (, ) Vertex: (, ) i) y = - 2 j) y = + 3 Vertex: (, ) Vertex: (, ) 30
Lastly, let s observe what happens when the coefficient changes in front of the absolute value of x. y= y = Compare the graphs from above. Make a conjecture about functions that come in the form: y = When y = the graph opens When y = the graph is opens (which means its reflected over the axis) y = y= Compare the graphs from above. Make a conjecture about functions that come in the form: y = When y = the graph is than y=. When the graph is than y=. 31
SUMMARY Exit Ticket 1. 2. 32
Homework Writing and Graphing Functions Day 4 4. 33
In examples 5 13, write an equation for each translation of y = 5. 9 units up 6. 6 units down 7. right 4 units 8. left 12 units 9. 8 units up, 10 units left 10. 3 units down, 5 units right 11. 12. 13. 34
In examples 14 and 15, identify the vertex and graph each. 14) y = 15) y = - 7 Vertex: (, ) Vertex: (, ) 16) On the set of axes below, graph and label the 17) On the set of axes below, graph and label the equations y = y = 2. equations y = y =. Explain how changing the coefficient of the absolute value from 1 to 2 affects the graph. Explain how changing the coefficient of the absolute value from 1 to affects the graph 35
Day 5 - Review of Relationships & Functions I. Analyzing Graphs II) Domain and Range 3) 4) 36
III) Identifying Functions Give the DOMAIN and RANGE of each relation. Tell whether the relation is a FUNCTION 5) 6) 7) Students (x) Field Trip Buses (y) 75 2 68 2 125 3 7 9 12-7 -1-3 {(1, 4), (2, 6), (1, 10), (6, 0)} 15 D: D: D: R: R: R: Function? Function? Function? IV) VERTICAL LINE TEST: Tell whether the relation is a FUNCTION 8) 9) 10) 11) 37
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V. Linear Functions 16) 17) Graph y 2x = 1 39
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Use the following graph below for problems #29 30. 29) Which statement best describes the translation of y = shown in the graph below. 30) 31) Graph the absolute value function below. y = Vertex: (, ) 43