22-23 Domain and Range Notes PDF

Unit 3 Day 2 Name: ____________________________ Date: __________________ Period: ______ Domain and Range Notes DOMAIN The set of all input values or the values of the independent variable (x-values). Values on the x-axis corresponding to act...

Unit 3 Day 2 Name: ____________________________ Date: __________________ Period: ______ Domain and Range Notes DOMAIN The set of all input values or the values of the independent variable (x-values). Values on the x-axis corresponding to actual points on the graph of the function. Domain / input / x-values / independent variable RANGE The set of all output values or the values of the dependent variable (y-values). Values on the y-axis corresponding to actual points on the graph of the funcion. Range / output / y-values / dependent variable Writing Domain and Range The way we write the domain and range depends on whether the graph is discrete (finite domain and range) or continuous (infinite domain and range). Domain and Range can be FINITE Separate, distinct points Written as a list of separate values Examples - list of ordered pairs, table, mapping, scatter plot (discrete graph) Domain and Range can be INFINITE Connected points (could draw without lifting your pencil) Written as a simple or compound inequality “All real numbers” if there are no restrictions Examples - lines and curves (continuous graphs) Sometimes it isn’t possible to list all the values that x or y can be because the graph is continuous and made up of an infinite number of points, like a line, ray or even a segment. In a continuous graph, to determine the domain, you should scan the x-axis from _____________________________. In a continuous graph, to determine the range, you should scan the y-axis from _____________________________. Example #1 - Table (Discrete) Does this table represent a function? What is the independent variable? Represent the domain in set builder notation: What is the dependent variable? Represent the range in set builder notation: Example #2 - Mapping (Discrete) Does this mapping represent a function? Represent the domain in set builder notation: Represent the range in set builder notation: Example #3 - Set of Ordered Pairs (Discrete) Example #4 - Set of Ordered Pairs (Discrete) {(9, 2), (3, 4), (2, 4), (3, 10), (1, 8)} {(-3, 5), (-2, 5), (-1, 5), (0, 5), (1, 5), (2, 5)} Does this set represent a function? Does this set represent a function? Represent the domain in set builder notation: Represent the domain in set builder notation: Represent the range in set builder notation: Represent the range in set builder notation: Example #5 - Graph (Discrete) Does this graph represent a function? What is the independent variable? What is the dependent variable? Represent the domain in set builder notation: Represent the domain in set builder notation: You can use interval notation OR set builder notation to represent the domain & range of continuous graphs. Regardless, we always write from least to greatest. For set-builder, use x for domain and y for range. If the endpoint is a CLOSED circle (included), then you use [ or ] For set-builder notation, [ or ] translates to ≤ or ≥ If there is no endpoint (-∞ or ∞) or the endpoint is an OPEN circle (not included), then you use ( or ) For set-builder notation, ( or ) translates to < or > Example #6 - Graph (Continuous) What is the least x-value? _________ Is it included? _________ What is the greatest x-value? _________ Is it included? _________ Represent the domain in set builder notation: What is the least y-value? _________ Is it included? _________ What is the greatest y-value? _________ Is it included? _________ Represent the range in set builder notation: Example #7 - Graph (Continuous) What is the least x-value? _________ Is it included? _________ What is the greatest x-value? _________ Is it included? _________ Represent the domain in set builder notation: What is the least y-value? _________ Is it included? _________ What is the greatest y-value? _________ Is it included? _________ Represent the range in set builder notation: Example #8 - Graph (Continuous) What is the least x-value? _________ Is it included? _________ What is the greatest x-value? _________ Is it included? _________ Represent the domain in set builder notation: What is the least y-value? _________ Is it included? _________ What is the greatest y-value? _________ Is it included? _________ Represent the range in set builder notation: Example #9 - Graph (Continuous) What is the least x-value? _________ Is it included? _________ What is the greatest x-value? _________ Is it included? _________ Represent the domain in set builder notation: What is the least y-value? _________ Is it included? _________ What is the greatest y-value? _________ Is it included? _________ Represent the range in set builder notation: Classwork - State the domain and range of the graphs in set builder notation. DOMAIN - Scan from left to right along the x-axis. RANGE - Scan from bottom to top along the y-axis. What is the least x-value? Is it included? What is the least y-value? Is it included? What is the greatest x-value? Is it included? What is the greatest y-value? Is it included? DOMAIN: DOMAIN: RANGE: RANGE: DOMAIN: DOMAIN: RANGE: RANGE: DOMAIN: DOMAIN: RANGE: RANGE:  DOMAIN: DOMAIN: RANGE: RANGE: Is the graph a function? What is the domain? What is the range? Is the table a function? What is the domain? What is the range? Is the mapping a function? What is the domain? What is the range?