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3.3 – Properties of Functions. Precal. Review increasing and decreasing:. Increasing function – up when going right Decreasing function – down when going right Constant – neither increasing nor decreasing (horizontal).

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## 3.3 – Properties of Functions

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**Review increasing and decreasing:**• Increasing function – up when going right • Decreasing function – down when going right • Constant – neither increasing nor decreasing (horizontal)**Determine the parts of the graph where the function is**increasing, decreasing, and/or constant • Increasing: • Decreasing: • Constant:**Local Extrema**• Extrema is the plural of extreme • This refers to where the graph reaches peaks and valleys • We call the “peaks” local maximums • We call the “valleys” local minimums**What is the local maximum of this function?**• Point A is a local maximum because the graph changes from increasing to decreasing at that point • It is only a LOCAL maximum instead of a global maximum because there are points on the graph higher (like point D)**What is the local minimum of this function?**• Point C is a local minimum because the graph changes from decreasing to increasing at that point • It is only a LOCAL minimum instead of a global minimum because there are points on the graph lower (like point F)**Identify the local extrema of the graph**• Local Minimums: • C, F, H • Local Maximums: • A, D, G**Partner Activity**• In a little bit you will follow these instructions: • Find a partner • One partner come up and grab a marker • Both partners find a spot at the board • Be prepared to graph some functions**Partner Roles**• The partner who got the marker is the “player” • The partner without the marker is the “coach” • When I give you the first problem, the coach is going to tell the player how to graph it • Players cannot draw anything unless the coachtells them to do so • Coaches cannot have the marker and draw**The “Big Ten”**• You are going to graph the ten most important base graphs of functions to remember • This is a part of section 3.4 (I have a handout for you on these graphs that you can use as notes)**Functions to graph (1)**• Graph f(x) = 1 • Is there any symmetry to this graph? • Can you reflect it over anything?**Functions to graph (2)**• Graph f(x) = x • Is there any symmetry to this graph? • Can you reflect it over anything?**Switch roles**• Give the marker to the other partner • The original “player” is now the “coach and vice versa**Functions to graph (3)**• Graph f(x) = x2 • Is there any symmetry to this graph? • Can you reflect it over anything?**Functions to graph (4)**• Graph f(x) = x3 • If the coach needs the help of a calculator, that is okay • Is there any symmetry to this graph? • Can you reflect it over anything?**Do you notice the pattern of symmetry?**• A function with an odd power reflects over the origin • A function with an even power reflects over the y-axis • Go write the red part of this slide in your notes for 3.3, then go back to the board • Switch player-coach roles again**Functions to graph (5)**• Graph • If the coach needs the help of a calculator, that is okay**Functions to graph (6)**• Graph • If the coach needs the help of a calculator, that is okay**Functions to graph (7)**• Graph • If the coach needs the help of a calculator, that is okay**Functions to graph (8)**• Graph • If the coach needs the help of a calculator, that is okay**Functions to graph (9)**• Graph • If the coach needs the help of a calculator, that is okay**Functions to graph (10)**• Graph • If the coach needs the help of a calculator, that is okay • This is the last one, so return the marker and head back to your seats when you are finished**Is this function odd, even, or neither?**• Even (reflects over the y-axis)**Is this function odd, even, or neither?**• Neither – it is not a function, even though it reflects over the x-axis**Is this function odd, even, or neither?**• Odd – it reflects over the origin

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