Name: Ammie Hamilton Date: September 6-­‐19 Subject: Algebra 3 Day 1 Sept 7 Wed Day 2 Sept 9 Friday Day 3 Sept 13 Tues Day 4 Sept 15 Thurs Day 5 Sept 19 Mon Learning Target I can determine the end behavior of functions by simply observing the function. I can determine the maximum number of turns a functions can have. I can match all 12 of the parent functions. I can perform basic transformations on all 12-­‐
parent functions. I can evaluate functions. I can determine inverse functions I can evaluate piece-­‐
wise functions I can graph piece-­‐wise functions. All LT’s for 1.5-­‐1.9 REVIEW DAY Common Core Standards A.8 – Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior). A.9 – Determine the end behavior of polynomial functions. A. 15 – Determine asymptotes and holes of rational functions, explain how each was found, and relate these behaviors to continuity. A. 18 – Find the composite of two given functions and find the inverse of a given function. Extend this concept to discuss the identity function f(x) = x. I can evaluate functions using the difference quotient. I can use composite functions. ! !!! !!(!)
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A.19 – Simplify complex algebraic fractions (with/without variable expressions and interger exponents) to include expressing as a single simplified fraction when f(x) = !
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for example. F.23 – Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. F.24 – Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. F.25 – Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. F.26 – Verify by composition that one function is the inverse of another. F.27 – Read values of an inverse function from a graph or a table, given that the function has an inverse. F. 28 – Produce an invertible function from a non-­‐invertible function by restricting the domain. G.35 – Graph piecewise defined functions and determine continuity or discontinuities G.36 – Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer). G.37 – Explain the effects of changing the parameters in transformations of functions. G.38 – Predict the shapes of graphs of exponential, logarithmic, rational, and piece-­‐wise functions, and verify then prediction with and without technology. G.39 – Relate symmetry of the behavior of even and odd functions. Bell Ringer ACT Problems on Canvas ACT Problems on Canvas Learning Plan 1.6 Parent Functions -­‐-­‐ Identify and graph linear and squaring functions. -­‐-­‐ Identify and graph cubic, square root, and reciprocal functions. -­‐-­‐ Identify and graph step and other piecewise-­‐fined functions. -­‐-­‐ Recognize graphs of parent functions. **Go ahead and evaluate functions** **Graph basic piece-­‐wise** Matching QUIZ – Parent Graphs 1.7 Transformations of Functions -­‐-­‐ Use vertical and horizontal shifts to sketch graphs of functions. -­‐-­‐ Use reflections to sketch graphs of functions. -­‐-­‐ Use nonrigid transformations to sketch graphs of functions. BIG Matching Session ACT Problems on Canvas ACT Problems on Canvas ACT Problems on Canvas QUIZ 1.9 Find inverse functions 1.8 Combinations of Functions: informally and verify that two Composite Functions functions are inverse functions LEAD OFF – Trial problems. Have of each other. them try some of each and see -­‐-­‐ Use graphs of functions to what they can do. determine whether functions -­‐-­‐ Add, subtract, multiply, and have inverse functions. divide functions. -­‐-­‐ Use the Horizontal Line Test -­‐-­‐ Find the composition of one to determine if functions are function with another function. one-­‐to-­‐one. **Domains of composite functions -­‐-­‐ Find inverse functions p. 86 Example 6 algebraically. -­‐-­‐ Use combinations and compositions of functions to model and solve real-­‐life problems.
Review for TEST – 1.5-­‐1.9 Name: Ammie Hamilton Date: September 6-­‐19 Subject: Algebra 3 Exit What is a parent function Slip/Closing referring to? BIG Matching Session – Graphs, functions, descriptions Math XL questions What does one-­‐to-­‐one mean? Study Guide Questions? Assessment Formative during class Observation Discussion Exit Ticket Formative during class Observation Discussion Exit Ticket Formative during class Observation Discussion Exit Ticket Formative during class Observation Discussion Exit Ticket Formative during class Observation Discussion Exit Ticket