1.1, 1.2 Linear and Piecewise Functions.pptx - CALCULUS 12 1.1 1.2 Functions and Analyzing Graphs of Functions Are these terms familiar to you

# 1.1, 1.2 Linear and Piecewise Functions.pptx - CALCULUS 12...

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1.1, 1.2 Functions and Analyzing Graphs of Functions Are these terms familiar to you? Polynomial / rational / radical / reciprocal / absolute value / trigonometric / exponential / logarithmic functions. 10/29/19 CALCULUS 12
Lesson Objective By the end of the lesson, I will be able to… To analyze functions and their graphs. Review knowledge from Pre-Calc 12
What will you need to understand calculus?1. What is a function? How do we represent them? Equations Tables Graphs Words
What will you need to understand calculus?2. How to determine domain and range3. How to use the vertical line test
Interval Notation Interval notation is another way of expressing domain and range. [ ] Includes endpoint ( ) Excludes endpoint
Piecewise Functions A function defined by two or more equations over a specific domain. Ex 1. Given f(x) = x + 1 if x ≤ 2 x 2 if x ˃ 2 Evaluate f(1), f(2) and f(3). Then sketch the graph.
Piecewise Functions Ex 2. Given f(x) = 1 if 0 ˂ x ≤ 1 2 if 1 ˂ x ≤ 2 3 if 2 ˂ x ≤ 3 4 if 3 ˂ x ≤ 4 Sketch the graph. This is also called a ‘step function’
Even functions are symmetric along the y-axis (line symmetry)If , then f is an even function.
Even and Odd Functions – More specific than before Odd functions are symmetric to the origin (point symmetry) If , then f is an odd function .
Ex3. Determine whether each of the following functions is even, odd or neither even nor odd.a) b) c) , even function, odd function
Increasing / Decreasing FunctionsWe say the function is: i.increasing on interval (a, b) ii.decreasing on (b, c) and iii.increasing again on (c, d)
Increasing / Decreasing FunctionsA function f is: increasingon an interval if whenever x1˂ x2in I.decreasingon an interval if whenever x1˂ x2in I.
Lesson Objective By the end of the lesson, I will be able to… To analyze functions and their graphs. Review knowledge from Pre-Calc 12
Suggested Practice Page 94 #39-57, 89, 91, 111-133 (Do only odd numbers.) Vocabulary: Interval notation, piecewise function, even and odd functions, increasing and decreasing functions.