relations and functions prepared by doron shahar
TRANSCRIPT
- Slide 1
- Relations and functions Prepared by Doron Shahar
- Slide 2
- 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