solution set (describes all values that make an equation true.) Functions f(x)=2x-7 Domain & Range solution set (describes all values that make an equation true.) Graphing an equation is the simplest way to recognize the solution set. g(x)=x+12

( horizontal number line) -5 5 10 -10 Positive #’s y-axis (vertical number line) RANGE negative #’s Positive #’s x-axis ( horizontal number line) negative #’s HORIZONTAL DOMAIN 2

y Range x Domain domain of the function ( set of values of x) range of the function (set of values of y ). y ≥ -3 Ex: Find the domain & range of the graph. x y 4 -4 Range Domain all real numbers. f (x) = x2 – 2x – 2 3

domain : all real numbers range :all real numbers. Graph y=5x. Looking at the graph of a function can help you determine its domain and range. All y-values y =5x All x-values domain : all real numbers range :all real numbers. 4

y Range (-3, 0) x Domain f (x) = Ex: Find the domain and range from its graph. domain : x ≥ -3 range is y ≥ 0 x y Range (-3, 0) Domain f (x) = 5

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

Range: y > 0 y =|x| Domain: ∞ or all real #s 7

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. Mapping Diagram Use x- & y-values to plot ordered pairs. x y Table x y 2 6 4 3 8 7 2 4 6 3 7 8 x-values under “x” y-values under “y”. Draw an arrow from each x-value to its corresponding y-value. Write all x-values under “x” & all y-values under “y”.

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)} YES YES NO YES 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. 10