ALGEBRA 1.8 Introduction to Functions

LEARNING TARGETS Language Goal  Students will be able to interpret a x and y coordinate plane using appropriate vocabulary. Math Goal  Students will be able to graph functions from ordered pairs. Essential Questions  What is the relationship between input and output in a function?

WARM-UP

GO OVER QUIZ

VOCABULARY The Coordinate Plane Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 x - axis y - axis Origin (0, 0) Ordered Pair (x, y) x-coordinate = the spaces you move left or right y-coordinate = the spaces you move up or down (+, +) (–, +) (–, –) (+, –)

VOCABULARY  Coordinate plane:  Axes:  Origin:  x – axis:  y – axis: Formed by the intersection of 2 perpendicular lines The two perpendicular lines of a coordinate plane. The point of intersection of the axes The horizontal number line (left - right) The vertical number line (up - down)

VOCABULARY  Ordered pair:  x – coordinate:  y – coordinate:  Quadrant:  Input:  Output: Consists of an x – coordinate and a y coordinate; written in the form (x, y) Tells how many units to move left or right from the origin Tells how many units to move up or down from the origin The axes divide the coordinate plan into 4 of these spaces In an equation that contains two variables, the value substituted for y In an equation that contains two variables, the value substituted for x

GUIDED NOTES  Label the coordinate plane with:  Quadrant 1, Quadrant 2, Quadrant 3, Quadrant 4, origin, x – axis, y – axis  An ordered pair consists of an x – coordinate and a y – coordinate.  Remember: x – coordinate moves left and right. y – coordinate moves up and down.

GUIDED NOTES EXAMPLE 1:  Graphing Points in the Coordinate Plane  Graph each point:  A. T(-4, 4)  B. U(0, -5)  C. V(-2, -3)  Your Turn!  A. R(2, -3)  B. S(0, 2)  C. W(-2, 6)

GUIDED NOTES EXAMPLE 2:  Locating Points in the Coordinate Plane  Name the ordered pair and quadrant in which each point lies.  A. E  B. F  C. G  D. H E F G H

GUIDED NOTES  An equation that contains two variables can be used as a rule to generate ordered pairs.  When you substitute a value for x, you generate a value for y.  The value substituted for x is called the input, and the value generated for y is called the output.  y = 10x + 5is a function!  In a function, the value of y (the output) is determined by the value of x (the input). All of the equations in this lesson represent functions.

GUIDED NOTES EXAMPLE 3:  An engraver charges a setup fee of $10 plus $2 for every word engraved. Write a rule for the engraver’s fee. Write ordered pairs for the engraver’s fee when there are 5, 10, 15, and 20 words engraved. Number of words engraved RuleChargesOrdered Pair x (input)y = xy (output)(x, y) Pattern =

GUIDED NOTES  When you graph ordered pairs generated by a function, they may create a pattern.  Usually the shape will be…  Line  U shaped  V shaped

GUIDED NOTES EXAMPLE 4A:  Generating and Graphing Ordered Pairs  Generate ordered pairs for the function using the given values for x.  Graph the ordered pairs  Describe the pattern.  y = 2x + 1; x = -2, -1, 0, 1, 2 InputOutputOrdered Pair xy(x, y) Pattern =

GUIDED NOTES EXAMPLE 4B: InputOutputOrdered Pair xy(x, y) Pattern =

LESSON QUIZ