Warm-up: page 32 Write the definition of a relation. A relation
is a correspondence between two sets A and B such that each element
of A corresponds to at least one element of B. The domain of a
relation is: The range of a relation is: Write the definition of a
function. A function is a relation such that each element of the
domain corresponds to exactly one element in the range. The set A.
The set B. Prepared by Doron Shahar
Slide 3
Relations in diagrams 3 1 0 3 1 2 Range Domain Relation 2 0 1 1
2 3 4 5 YesNo Yes Is it a function? Range Domain Relation Is it a
function? Prepared by Doron Shahar
Slide 4
3.1.1(A) Relations in Tables Determine whether the following
represents y as a function of x. x-3013 y22222 3 1 0 3 1 2 Yes
Range Domain Is it a function? If none of the x-values is repeated,
then the table represents y as a function of x. Prepared by Doron
Shahar
Slide 5
3.1.1(B) Relations in Tables Determine whether the following
represents y as a function of x. x-2 011 y45123 No Range Domain Is
it a function? If at least one of the x-values is repeated, then
the table does not represent y as a function of x. 2 0 1 1 2 3 4 5
Prepared by Doron Shahar
Slide 6
3.1.2 Relations in Graphs Determine whether the following
represent y as a function of x. (A)(B) A graph represents the graph
of a function if and only if no vertical line passes through the
graph more than ________. Function Not a function Prepared by Doron
Shahar
Slide 7
3.1.3 Relations in Equations Determine whether the following
represent y as a function of x. Steps: 1) Solve for y 2) Plug in
trial values for x If for some value of x there is more than one y
value, then the equation does not represent y as a function of x.
If for all values of x there is only one y value, then the equation
represents y as a function of x. Prepared by Doron Shahar
Slide 8
3.1.3(C) Relations in Equations Determine whether the following
represents y as a function of x. 1) Solve for y 2) Plug in trial
values for x Starting Equation Solution for y If x=5, If x=9, There
is a value of x, namely x=9, for which there are two corresponding
y values: +2 and 2. y is NOT a function of x. Prepared by Doron
Shahar
Slide 9
3.1.3(A) Relations in Equations Determine whether the following
represents y as a function of x. 1) Solve for y 2) Plug in trial
values for x Starting Equation Solution for y If x=0, There is a
value of x, namely x=0, for which there are two corresponding y
values: +3 and 3. y is NOT a function of x. Subtract x 2 Take
square root Prepared by Doron Shahar
Slide 10
3.1.3(D): Relations in Equations Determine whether the
following represents y as a function of x. 1) Solve for y 2) Plug
in trial values for x Starting Equation Solution for y If x=7, For
each value of x, there is only one corresponding y value. y is a
function of x. Divide by x Take cube root Prepared by Doron
Shahar
Slide 11
3.1.3(B) Relations in Equations Determine whether the following
represents y as a function of x. 1) Solve for y 2) Plug in trial
values for x Starting Equation Solution for y If x=3, Factor out y
Divide by (x4) For each value of x, there is only one corresponding
y value. y is a function of x. Prepared by Doron Shahar
Slide 12
3.1.6 Review (B) Create a table of values for x and y so that y
is NOT a function of x. (C) Create a graph which does NOT represent
y as a function of x. (A) Create an equation in x and y so that y
is NOT a function of x. Prepared by Doron Shahar
Slide 13
Warm-up Write the following using interval notation. 13 < x
5 r 3.6 y < 2 All real numbers All real numbers except x = 3 All
real numbers except x = 2 and x = 4 Prepared by Doron Shahar
Slide 14
Interval notation Write the following using interval notation.
13 < x 5 r 3.6 y < 2 Endpoint not included Endpoint included
Mnemonic : 3.6 r < Mnemonic: < y
