Algebra 2 Foundations, pg 64  Students will be able to graph relations and identify functions. Focus Question What are relations and when is a relation a function?  A relation is a set of pairs of input and output values.  A function is a relation in which each input corresponds with exactly one output.

Algebra 2 Foundations, pg 64  Students will be able to graph relations and identify functions. You can use mappings to describe relationships between sets of numbers. You can represent a relation in four different ways as shown above.

 Students will be able to graph relations and identify functions.

The domain of a relation is the set of inputs, also called x- coordinates, of the ordered pairs. The range is the set of outputs, also called y-coordinates, or the ordered pairs. Algebra 2 Foundations, pg 66

 Students will be able to graph relations and identify functions. A function is a relation in which each element of the domain corresponds to exactly one element of the range. Algebra 2 Foundations, pg 67

 Students will be able to graph relations and identify functions. You can use the vertical-line test to determine whether a relation is a function. The vertical-line test states that if any vertical line passes through more than one point on the graph of a relation, then the relation is not a function. *Here’s Why It Works* If a vertical line passes through a graph at more than one point, there is more than one value in the range that corresponds to a value in the domain. For example, the graph shows that there are two output values, y 1 and y 2, that both correspond to input value x. This relation is not a function. Algebra 2 Foundations, pg 67

 Students will be able to graph relations and identify functions. Algebra 2 Foundations, pg 67

 Students will be able to graph relations and identify functions. Algebra 2 Foundations, pg 67

 Students will be able to graph relations and identify functions. List the domain (x) and range (y) of each relation. 1.{(3, -2), (4, 4), (0, -2), (4, 1), (3, 2)} 2.{(0, 4), (4, 0), (-3, -4), (-4, -3)} Determine whether each relation is a function. 3.{(3, -8), (-9, 1), (3, 2), (-4, 1), (-11, -2)} 4.{(1, 1), (2, 0), (3, 1), (4, 3), (0, 2)} Domain: {0, 3, 4} Range: {-2, 1, 2, 4} Domain: {-4, -3, 0, 4} Range: {-4, -3, 0, 4} No. There are two x-coordinates that are the same. Yes. Each x value has only one corresponding y value.

 Students will be able to graph relations and identify functions.

With your group or partner, complete

Algebra 2 Foundations, pg 70  Students will be able to write and evaluate functions. Focus Question Why are function rules useful?  You use function rules to find the output (y-value) when given the input (x-value).

Algebra 2 Foundations, pg 70  Students will be able to write and evaluate functions. A function rule is an equation that represents an output value in terms of an input value. You can write a function rule in function notation. Shown below are examples. The independent variable, x, represents the input of the function. The dependent variable, f(x), represents the output of the function (y). It is called the dependent variable because it depends on the input value.

Algebra 2 Foundations, pg 70  Students will be able to write and evaluate functions.

Algebra 2 Foundations, pg 71  Students will be able to write and evaluate functions. To model a real world situation using a function rule, you need to identify the dependent and independent quantities. One way to describe the dependence of a variable quantity is to use a phrase such as, “distance is a function of time.” This means that distance depends on time.

Algebra 2 Foundations, pg 71  Students will be able to write and evaluate functions.