PC smart 1.1 PDF

PC smart 1.1 August 24, 2024 Chapter 1 Fundamentals 1.1 Real Numbers G. Patkar PC smart 1.1 August 24, 2024 Objectives Real Numbers Properties of Real Numbers...

PC smart 1.1 August 24, 2024 Chapter 1 Fundamentals 1.1 Real Numbers G. Patkar PC smart 1.1 August 24, 2024 Objectives Real Numbers Properties of Real Numbers Addition and Subtraction Multiplication and Division The Real Line Sets and Intervals Absolute Value and Distance Vocabulary: Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers (The set denoted by ) G. Patkar PC smart 1.1 August 24, 2024 Vocabulary: Repeating/Non­repeating decimals Commutative / Associative / Distributive Properties G. Patkar PC smart 1.1 August 24, 2024 Sets and Intervals: We can write A in set­builder notation as which is read “A is the set of all x such that x is an integer and 0 < x < 7.” We can also use interval notation like (0,7). Sometimes, we represent the answer as union or intersection of two or more sets. Union: If S and T are sets, then their union is the set of all elements in S or T (or in both). Intersection: The intersection of S and T is the set of all elements in both S and T. The empty set, denoted by is the set that contains no element. G. Patkar PC smart 1.1 August 24, 2024 Open Interval Closed Interval interval notation Set builder notation Open parentheses ( ) and Square brackets [ ] and solid open circles on the graph circles on the graph means means endpoints are excluded endpoints are included. G. Patkar PC smart 1.1 August 24, 2024 Intervals may also include one endpoint but not the other, or they may extend infinitely far in one direction or both. The following table lists the possible types of intervals. Try to write interval notation for these graphical representations. G. Patkar PC smart 1.1 August 24, 2024 G. Patkar PC smart 1.1 August 24, 2024 G. Patkar PC smart 1.1 August 24, 2024 G. Patkar PC smart 1.1 August 24, 2024 Write in interval notation: G. Patkar PC smart 1.1 August 24, 2024 Write in interval notation: Absolute Value and Distance G. Patkar PC smart 1.1 August 24, 2024 = absolute value of a number a = distance from a to 0 DEFINITION OF ABSOLUTE VALUE If a is a real number, then the absolute value of a is G. Patkar PC smart 1.1 August 24, 2024 G. Patkar PC smart 1.1 August 24, 2024 Piecewise Function: G. Patkar PC smart 1.1 August 24, 2024 Graph the function. Describe the domain and range. 7. y = −x, if x > 0 x + 1, if x ≤ 0 Graph the function. Describe the domain and range. 7. y = −x, if x > 0 x + 1, if x ≤ 0 G. Patkar PC smart 1.1 August 24, 2024 G. Patkar PC smart 1.1 August 24, 2024 Write a piecewise function for the graph. Write a piecewise function for the graph. G. Patkar PC smart 1.1 August 24, 2024 Graph the function. Also write as piecewise function. f(x) = l x+2 l Graph the function. Also write as piecewise function. f(x) = l x+2 l G. Patkar PC smart 1.1 August 24, 2024 Graph the function. Also write as piecewise function. f(x) = l x+2 l Rewrite the function without absolute value notation/ as a piecewise function. G. Patkar PC smart 1.1 August 24, 2024 Rewrite the function without absolute value notation/ as a piecewise function. Graph the function. Describe the domain and range. G. Patkar PC smart 1.1 August 24, 2024 G. Patkar PC smart 1.1 August 24, 2024 Writing absolute Value Function as a Piecewise Function: Every absolute value function can be written as a piecewise function Work with your partner. Graph Rewrite as a piecewise function. Why is x = 3 the “breakpoint”? When x > 3, is equal to (x – 3) or (3 – x)? Test out with some numbers. When x < 3, is equal to (x – 3) or (3 – x)? G. Patkar PC smart 1.1 August 24, 2024 Writing absolute Value Function as a Piecewise Function: Every absolute value function can be written as a piecewise function Work with your partner. Graph Rewrite as a piecewise function. Why is x = 7 the “breakpoint”? When x > 7, is equal to (x – 7) or (7 – x)? Test out with some numbers. When x < 7, is equal to (x – 7) or (7 – x)? G. Patkar PC smart 1.1 August 24, 2024 Rewrite the function without absolute value notation/ as a piecewise function. Rewrite the function without absolute value notation/ as a piecewise function. G. Patkar PC smart 1.1 August 24, 2024 Rewrite the function without absolute value notation/ as a piecewise function. G. Patkar PC smart 1.1 August 24, 2024 Practice: Rewrite the function without absolute value notation/ as a piecewise function. Practice: Rewrite the function without absolute value notation/ as a piecewise function. G. Patkar PC smart 1.1 August 24, 2024 Practice: Rewrite the function without absolute value notation/ as a piecewise function. G. Patkar PC smart 1.1 August 24, 2024 Practice: Rewrite the function without absolute value notation/ as a piecewise function. G. Patkar PC smart 1.1 August 24, 2024 Practice: Rewrite the function without absolute value notation/ as a piecewise function. Practice: Rewrite the function without absolute value notation/ as a piecewise function. G. Patkar PC smart 1.1 August 24, 2024 https://www.youtube.com/watch?v=p02y9ZRgZmw&ab_channel=JeremyKlassen Write as a piecewise function: G. Patkar PC smart 1.1 August 24, 2024 Write as a piecewise function: Write as a piecewise function: G. Patkar PC smart 1.1 August 24, 2024 Write as a piecewise function: Write as a piecewise function: G. Patkar PC smart 1.1 August 24, 2024 Write as a piecewise function: Write as a piecewise function: G. Patkar PC smart 1.1 August 24, 2024 G. Patkar PC smart 1.1 August 24, 2024 HW (1.1): pg 11 #41 to 84 (even) G. Patkar