Updates- Quiz 1 will be on Tuesday, January 13th
- Unit 1 Test will be on Tuesday, Jan. 20th
Bell Ringer QuizWhat are functions? a mathematical relationship in which any input has one and only one output a mathematical relationship in which any input has two or more outputs a mathematical relationship in which any input has at least one output a mathematical relationship in which any output has at least one input none of the above Determine which relation is a function. If, then find f(-2). 5 -3 3 -1 none of the above What is the x and y-intercept of ? x-intercept: (2,0) | y-intercept: (0,-8) x-intercept: (0,2) | y-intercept: (-8,0) x-intercepts: (-2,0) and (2,0) | y-intercept: (0,-8) x-intercept: (4,0) | y-intercept: (0,-8) none of the above Find the domain and range of the following: D: [-3,2) | R: (-5,2) D: (-3,2) | R: (-5,2] D: [-3,2] | R: (-5,2] D: [-3,2) | R: (-5,2] - none of the above
Review- Intro to Functions
- What is a function?
- Function Notation
- Evaluating Functions
- Examples/Counterexamples
- Graph
- Table
- Set
- Domain/Range (using functions students covered in Algebra: linear, constant, square root, etc.)
- Graph
- Table
- Set
- Using Words
- Compound Inequalities
- Interval Notation
- Intercepts
Lesson- Intervals Of Increasing And Decreasing (Quadratic and Absolute Value Functions)
- Extrema
- Relative Min/Max (Cubic Functions)
- Absolute Min/Max (Quadratic and Absolute Value Functions)
- Using the graphing calculator to calculate mins and maxs
- Note: Address issue with rounding using the calculator
- Symmetry
- Axis of Symmetry (Quadratic and Absolute Value Functions)
- End Behavior
- Evaluating Functions
- Function Operations
- Addition, Subtraction, Multiplication, Division
- Composition
- Translations
- Checkpoints
Exit Ticket- Posted on board at the end of the block
| Lesson Objective(s)- How is end behavior of a function determined?
- How are extrema found using a graphing calculator?
Standard(s)- CC.9-12.F.IF.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
- CC.9-12.F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- CC.9-12.F.IF.6 Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
- CC.9-12.F.IF.7 Analyze functions using different representations. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
- CC.9-12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.*
- CC.9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.*
- CC.9-12.F.IF.8 Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- CC.9-12.F.IF.9 Analyze functions using different representations. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
- CC.9-12.F.BF.1c (+) Compose functions.
- CC.9-12.F.BF.3 Build new functions from existing functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
- CC.9-12.F.LE.2 Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Mathematical Practice(s)- #1 - Make sense of problems and persevere in solving them
- #2 - Reason abstractly and quantitatively
- #4 - Model with mathematics
- #5 - Use appropriate tools strategically
- #7 - Look for and make use of structure
Past Checkpoints |