2.1 Notes – Represent Relations and Functions

A pairing of input and output values Relation Domain Range Function A pairing of input and output values Input values (x) Write from smallest to largest, don’t repeat! Output values (y) Write from smallest to largest, don’t repeat! Every x value has exactly one y value

Domain:_____________ Range: ______________ –3, –1, 3, 5 –3 –4 –4, –2, 1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. a. D R Domain:_____________ Range: ______________ –3, –1, 3, 5 –3 –4 –4, –2, –1, 3 –1 –2 Function YES NO 3 –1 Every x value has exactly one y value 5 3

Domain:_____________ Range: ______________ –5, –1, 3, 4 –5 –5 –5, –2, 1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. b. D R Domain:_____________ Range: ______________ –5, –1, 3, 4 –5 –5 –5, –2, 4 –1 –2 Function YES NO 3 4 Every x value has exactly one y value 4

Domain:_____________ Range: ______________ –4, 4, 5 –4 –2 –2, 1, 2, 5 1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. c. D R Domain:_____________ Range: ______________ –4, 4, 5 –4 –2 –2, 1, 2, 5 4 1 Function YES NO 5 2 4 has two y values 5

Domain:_____________ Range: ______________ –2, –1, 0, 1, 2 –2 –4 –4 –1 1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. x –2 –1 1 2 y –4 d. D R Domain:_____________ Range: ______________ –2, –1, 0, 1, 2 –2 –4 –4 –1 Function YES NO 1 Every x value has exactly one y value 2

Domain:_____________ Range: ______________ 1 1 1 1, 2, 4, 7 2 1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. e. D R Domain:_____________ Range: ______________ 1 1 1 1, 2, 4, 7 2 Function YES NO 4 1 has four y values 7

Domain:_____________ Range: ______________ –2, –1, 0, 1, 2 –2 1 1, 2, 1. Identify the domain and range of the given relation. Then represent the relation using a mapping diagram. Is the relation a function? Explain. x –2 –1 1 2 y 4 f. D R Domain:_____________ Range: ______________ –2, –1, 0, 1, 2 –2 1 1, 2, 4 –1 2 Function YES NO 4 1 Every x value has exactly one y value 2

Has two variables with exponents of one. Function notation Linear Equation f(x) Same thing as “y” f “at” x NOT f times x!!!!!! f(5) means x = 5 Has two variables with exponents of one.

The values that x can be. The values that y can be. Domain for equations Range for equations The values that x can be. All x “such that” x is the set of numbers The values that y can be. All y “such that” y is the set of numbers

once NOT Function Not a Function Vertical Line Test Given any vertical line, if it crosses the graph _______ it is a function. If it crosses the graph more than once it is ______ a function! once NOT Function Not a Function

a. Linear f(–1) = –4 – 2(–1) = –4 + 2 f(–1) = –2 2. Tell whether the function is linear. Then evaluate the function. a. Linear f(–1) = –4 – 2(–1) = –4 + 2 f(–1) = –2

b. Not Linear g(0) = (0)2 – 1 = 0 – 1 g(0) = –1 2. Tell whether the function is linear. Then evaluate the function. b. Not Linear g(0) = (0)2 – 1 = 0 – 1 g(0) = –1

Domain:_____________ Range: ______________ 3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning. Domain:_____________ Range: ______________ Function YES NO Vertical line test

Domain:_____________ Range: ______________ 3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning. Domain:_____________ Range: ______________ Function YES NO Vertical line test

Domain:_____________ Range: ______________ 3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning. Domain:_____________ Range: ______________ Function YES NO Vertical line test

Domain:_____________ Range: ______________ 3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning. Domain:_____________ Range: ______________ Function YES NO Vertical line test

Domain:_____________ Range: ______________ 3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning. Domain:_____________ Range: ______________ Function YES NO Vertical line test

Domain:_____________ Range: ______________ 3. Find the domain and range. Then determine if the relation is a function. Explain your reasoning. Domain:_____________ Range: ______________ Function YES NO Vertical line test

a. D:_____________ R: ______________ 4. Graph the function. Then state the domain and range. a. D:_____________ R: ______________

Vertex: (–3, –1) b. –b 2a –(6) 2(1) x = = = –3 y = (–3)2 + 6(–3) + 8 4. Graph the function. Then state the domain and range. Vertex: (–3, –1) b. –b 2a –(6) 2(1) x = = = –3 y = (–3)2 + 6(–3) + 8 y = –1

b. x 4 x 2 (x + 4)(x + 2) = 0 x = –4, –2 D:_____________ 4. Graph the function. Then state the domain and range. b. x 4 x 2 (x + 4)(x + 2) = 0 x = –4, –2 D:_____________ R: ______________

Vertex: (2, 9) c. –b 2a –(4) 2(-1) x = = = 2 y = –(2)2 + 4(2) + 5 4. Graph the function. Then state the domain and range. Vertex: (2, 9) c. –b 2a –(4) 2(-1) x = = = 2 y = –(2)2 + 4(2) + 5 y = 9

c. x -5 x 1 –(x – 5)(x + 1) = 0 x = 5, –1 D:_____________ 4. Graph the function. Then state the domain and range. c. x -5 x 1 –(x – 5)(x + 1) = 0 x = 5, –1 D:_____________ R: ______________

Max # of turns: _________ Right End Behavior: _____ 4. Graph the function. Then state the domain and range. d. Max # of turns: _________ Right End Behavior: _____ Left End Behavior: ______ x – intercepts: __________ y – intercepts: __________ 2 ↑ ↓

( )( ) x2 (x + 2) –1( x + 2) (x2 – 1)(x + 2) x 1 x –1 (x + 1)(x – 1)(x + 2) = 0 –1, 1, –2 x – intercepts: _________

D:_____________ R: ______________ Max # of turns: _________ Right End Behavior: _____ Left End Behavior: ______ x – intercepts: __________ y – intercept(s): __________ 2 ↑ ↓ D:_____________ R: ______________ –1, 1, –2 –2

domain: ____________________ 5. State the domain of each function: a. domain: ____________________

domain: ____________________ 5. State the domain of each function: b. domain: ____________________

domain: ____________________ 5. State the domain of each function: c. domain: ____________________

domain: ____________________ 5. State the domain of each function: d. domain: ____________________