1-1. Functions. Lesson 1-1. What You ll Learn. Active Vocabulary. Scan Lesson 1-1. Write two things that you already know about functions.

Transcription

1 1-1 Functions What You ll Learn Scan Lesson 1- Write two things that ou alread know about functions. Lesson 1-1 Active Vocabular New Vocabular Write the definition net to each term. domain dependent variable function independent variable range relation Chapter 1 3 Glencoe Precalculus

2 Lesson 1-1 (continued) Main Idea Details Describe Subsets of Real Numbers pp. 4 5 Complete the table. Write each set of numbers in set-builder and interval notation, if possible. Set {-2, -1, 0, 1, } Set-Builder Notation Interval Notation 4-5 < 22 < -4 or > 6 all multiples of 7 Identif Functions pp. 5 8 Determine whether each relation represents as a function of. Write es or no. {(2, -4), (-3, 7), (23, -5), (-3, 10)} The input value is a Social Securit number and the output value is the owner s first name = Chapter 1 4 Glencoe Precalculus

3 1-2 Analzing Graphs of Functions and Relations What You ll Learn Scan the Eamples for Lesson 1- Predict two things that ou think ou will learn about functions and their graphs. Active Vocabular even function New Vocabular Match the term with its definition b drawing a line to connect the two. the -intercept(s) of the graph of a function Lesson 1-2 line of smmetr odd function point smmetr roots functions that are smmetric with respect to the origin graphs that have this propert can be rotated 180 with respect to a point and appear unchanged the solution(s) of a given equation functions that are smmetric with respect to the -ais zeros graphs that have this propert can be folded along a line so that the two halves of the graph match eactl Chapter 1 5 Glencoe Precalculus

4 Lesson 1-2 (continued) Main Idea Details Analzing Function Graphs pp Use the graph of each function to find its -intercept and zeros. -intercept: zeros: -intercept: zeros: Smmetr of Graphs pp Identif which function is even, which is odd, and which is neither. f() = 3 - g() = h() = Helping You Remember Think about the different tpes of line smmetr: about the -ais, about the -ais, and about the origin. Provide eamples of graphs illustrating each of the smmetries. -ais smmetr -ais smmetr 3. origin smmetr Chapter 1 6 Glencoe Precalculus

5 1-3 Continuit, End Behavior, and Limits What You ll Learn Scan the tet in Lesson 1-3. Write two facts that ou learned about continuit. Active Vocabular New Vocabular Write the correct term net to each definition. a function that has no breaks, holes, or gaps in its graph a concept describing how a function behaves at either end of its graph a function is said to have this form of a discontinuit at = c if the absolute value of the function increases or decreases indefinitel as the -values approach c from the left and the right the concept of approaching a value without necessaril ever reaching it a function is said to have this form of discontinuit at = c if the function is continuous everwhere ecept for a hole at = c Lesson 1-3 a function that is not continuous a function is said to have this form of discontinuit at = c if the limits of the function as approaches c from the left and the right eist but have two distinct values Chapter 1 7 Glencoe Precalculus

6 Lesson 1-3 (continued) Main Idea Details Continuit pp Complete the table b providing our own verbal description of each tpe of discontinuit. Then provide an eample to illustrate our verbal description. Discontinuit Verbal Description Eample Infinite Jump Discontinuit End Behavior pp Removable or Point Use the graph of f () = to describe its end behavior. Chapter 1 8 Glencoe Precalculus

7 1-4 Etrema and Average Rates of Change What You ll Learn Scan the tet under the Now heading. List two things that ou will learn in this lesson. Active Vocabular constant decreasing increasing maimum minimum New Vocabular Label the diagram with the terms listed at the left. 2 Lesson 1-4 secant line Chapter 1 9 Glencoe Precalculus

8 Lesson 1-4 (continued) Main Idea Details Increasing and Decreasing Behavior pp Draw the graph of a function modeling the indicated behavior throughout its domain. Increasing Function Decreasing Function Constant Function Average Rate of Change pp Find the average rate of change of f() = on the interval [-1, 2]. Slope formula Substitute -1 for 1 and 2 for 2. Evaluate f(3) and f(-2). Simplif. Chapter 1 10 Glencoe Precalculus

9 1-5 Parent Functions and Transformations What You ll Learn Scan Lesson 1-5. Predict two things that ou epect to learn based on the headings and Ke Concept boes. Active Vocabular New Vocabular Fill in each blank with the correct term. absolute value function identit function parent function reflection transformations translation A(n) is a rigid transformation that has the affect of shifting the graph of a function up, down, left, or right. A(n) functions in a famil. is the simplest of the A(n) is a rigid transformation which produces a mirror image of the graph of a function with respect to a specific line. The points with coordinates (a, a). f () = passes through all A(n) of a parent function affects the appearance of the parent graph. The V-shaped function., denoted as f () =, is a Lesson 1-5 Chapter 1 11 Glencoe Precalculus

10 Lesson 1-5 (continued) Main Idea Details Parent Functions pp Each graph is the parent function for a famil of functions. Identif the parent function. Transformations pp Define the three different transformations introduced in this lesson. Translation Reflection Dilation Chapter 1 12 Glencoe Precalculus

11 1-6 Function Operations and Composition of Functions What You ll Learn Scan Lesson 1-6. List two headings that ou would use to make an outline of this lesson. Lesson 1-6 Active Vocabular Review Vocabular Define function in our own words. (Lesson 1-1) function relation roots composition Define relation in our own words. (Lesson 1-1) Define roots in our own words. (Lesson 1-2) New Vocabular Write the definition net to the term. Chapter 1 13 Glencoe Precalculus

12 Lesson 1-6 (continued) Main Idea Details Operations with Functions pp Given f () = and g () = 4 2-1, find each function and its domain. (f + g)() = Domain: (f g)() = Domain: 3. (f g)() = Domain: 4. ( g) f () = Domain: Composition of Functions pp Given f () = + 1, g() = 2 2, and h() = , find each composition. [ f g ] () = g [ f () ] = Helping You Remember 3. [ h f ] () = In the composition f g, which is read as f composition g or f of g, the function g is applied first then f. Think of a mnemonic device for remembering how to find the composition of two functions f and g so that ou are not confused when ou see f g or g f. Chapter 1 14 Glencoe Precalculus

13 1-7 Inverse Relations and Functions What You ll Learn Scan the Eamples for Lesson 1-7. Predict two things that ou think ou will learn about inverse relations. Active Vocabular Review Vocabular Define domain in our own words. (Lesson 1-1) domain Define range in our own words. (Lesson 1-1) Lesson 1-7 range inverse relations inverse function New Vocabular Fill in each blank with the correct term or phrase. If a function passes the horizontal line test, then it is said to be, because no -value is matched with more than one -value and no -value is matched with more than one -value. Two relations are if and onl if one relation contains the element (b, a) whenever the other relation contains the element (a, b). one-to-one If the inverse relation of a function f is also a function, then it is called the of f. Chapter 1 15 Glencoe Precalculus

14 Lesson 1-7 (continued) Main Idea Details Inverse Functions pp Graph each function using a graphing calculator, and appl the horizontal line test to determine whether its inverse function eists. Write es or no. f () = g () = 2-3. h() = g () = f () = Find Inverse Functions pp Find the inverse of f () = Original function Replace f () with. Helping You Remember Echange and. Solve for. Replace with f 1 (). In Lesson 1-6, ou learned how to find the composition of two functions. Eplain what role the composition of functions plas in determining whether two functions are inverses of one another. Chapter 1 16 Glencoe Precalculus