Domain Range solution set describes all values that

Domain & Range solution set (describes all values that make an equation true. ) • Graphing an equation is the simplest way to recognize the solution set.

Positive #’s -5 ( horizontal number line) HORIZONTAL DOMAIN Positive #’s 0 negative #’s -10 x-axis RANGE negative #’s y-axis (vertical number line) 5 -5 5 10

domain of the function ( set of values of x) range of the function (set of values of y ). Ex: Find the domain & range of the graph. y Range Domain all real numbers. 4 -4 y ≥ -3 f (x) = x 2 – 2 x – 2 x

Graph y=5 x. Looking at the graph of a function can help you determine its domain and range. y =5 x All y-values All x-values domain : all real numbers range : all real numbers.

Ex: Find the domain and range from its graph. domain : x ≥ -3 range is y ≥ 0 y Range (-3, 0) x Domain f (x) =

Identifying Functions Give the domain and range of the relation. Tell whether the relation is a function. Explain. Range Domain x y Draw in lines to see the domain and range values. D: – 5 ≤ x ≤ 3 R: – 2 ≤ y ≤ 1 To compare domain & range values, make a table using the points from the graph. – 2 – 1 – 2 1 1 The relation is not a function. Nearly all domain values have more than one range value. Helpful Hint To find the domain & range from a graph, it may help to draw lines to see the x- and y-values.

y =|x| Range: y > 0 Domain: ∞ or all real #s

Showing Multiple Representations of Relations Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Table x y 2 3 4 7 6 8 Use x- & y-values to plot ordered pairs. Write all x-values under “x” & all yvalues under “y”. Mapping Diagram y x 2 3 4 7 6 8 x-values under “x” y-values under “y”. Draw an arrow from each x-value to its corresponding y-value.

Is the relation a function? • {(2, 4), (3, 6), (4, 8)} • {(2, 4), (3, 4), (4, 4)} • {(2, 4), (2, 6), (2, 8)} • {(2, 5), (3, 7), (4, 9)}

Relations Different ways to represent a relation. GIVEN: {(3, 3), (-1, 4), (0, -4)} Ordered Pairs Table Graph Mapping (3, 3) (-1, 4) (0, -4) • mapping - an illustration how each element of domain is paired with an element in the range.