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Pre-Cal

Pre-Cal. Chapter 1 Functions and Graphs Section 1.3 and 1.4. The Twelve Basic Functions. Turn to pg. 102 in your book and sketch each of the twelve basic functions they have illustrated there and be sure to label your sketch with the appropriate equation. Section 1.4 Definitions.

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Pre-Cal

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  1. Pre-Cal Chapter 1 Functions and Graphs Section 1.3 and 1.4

  2. The Twelve Basic Functions • Turn to pg. 102 in your book and sketch each of the twelve basic functions they have illustrated there and be sure to label your sketch with the appropriate equation.

  3. Section 1.4 Definitions • Relation: A set of ordered pairs. • Implicitly: just a fancy way of saying to represent completely.(This is when you take an equation that is not a function and write it as 2 separate pieces such that each piece separately is a function. • Parameter: a given value that is plugged into a set of equations to find the x and y value of a relation.

  4. Definitions Cont. • Inverse Relation: this is found by switching the x value of a relation to the y value and vice versa. • One-to-One: this is what we call a function whose inverse also turns out to be a funcion. • Inverse Function: you get this by switching the x and y in the original function equation and then solving for y to get your new equation. • Reflections: a function and its inverse are reflections of each other if they are one-to-one.

  5. Clarification • One thing you need to know that I may not have explained well enough is that in order for a graph to be even it must be symmetric with the y-axis. • In order for a graph to be odd it must be symmetric with the origin.

  6. Function Operations • Sum: (f + g)(x) = f(x) + g(x) • Difference: (f – g)(x) = f(x) – g(x) • Product: (fg)(x) = f(x)g(x) • Quotient: (f/g)(x) = f(x)/g(x); g(x) ≠ 0 • The domain of the new function is the combination of the domains of each of the functions involved.

  7. Function Operations Cont. • Composition f of g: (f o g)(x) = f(g(x)) means to take whatever equation or number g(x) is and replace all of the x variables in f(x) and simplify.

  8. Examples

  9. Homework • Pg. 109(1-21) • Pg.

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