Unit 3: Functions Topics: Function vs. Relation Function Notation: Part 1
Relation def – A relation is any set of ordered pairs. A relation is an assignment between input values and their corresponding output values.
In order for a relation to be a function… EVERY INPUT MUST HAVE AN OUTPUT TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT ONE INPUT CAN HAVE ONLY ONE OUTPUT INPUT (DOMAIN) FUNCTION MACHINE OUTPUT (RANGE)
Function Notation “f of x” domain Input = x independent Output = f(x) = y independent range dependent
Example: Just Look & Listen Which of the following relations are functions? R= {(9,10), (-5, 10), (2, 10)} S= {(6, a), (8, f), (6, b)} T= {(z, 7), (y, -5), (r, 7) (z, 0), (k, 0)} write this down No two ordered pairs can have the same first coordinate (and different second coordinates).
Is this a function? 1. {(2,5) , (3,8) , (4,6) , (7, 20)} 2. {(1,4) , (1,5) , (2,3) , (9, 28)} 3. {(1,0) , (4,0) , (9,0) , (21, 0)}
The Vertical Line Test If it is possible for a vertical line to intersect a graph at more than one point, then the graph is NOT the graph of a function. Page
Examples I’m going to show you a series of graphs. Determine whether or not these graphs are functions. Draw sketches of the graphs in your notes.
YES! Function? #1
#2 Function? YES! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals Another cool function: abs(x) + 2sin(x)
#3 Function? NO! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals Another cool function: abs(x) + 2sin(x)
#4 Function? YES! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals Another cool function: abs(x) + 2sin(x)
#5 Function? NO!
YES! Function? #6 This is a piecewise function
Function? #7 NO! D: all reals R: [0, 1] Another cool function: y = sin(abs(x)) Y = sin(x) * abs(x)
#8 Function? NO! Y = 0.5x + 2 + 2sin(x) D: all reals R: all reals Another cool function: abs(x) + 2sin(x)
YES! #9 Function?
Function? #10 YES!
Function? #11 NO! D: [-3, -1) U (-1, 3] R: {-1, 1}
YES! Function? #12 D: [-3, -1) U (-1, 3] R: {-1, 1}