Thinking Mathematically

Algebra: Graphs, Functions and Linear Systems

7.1 Graphing and Functions

Graphing

• Cartesian coordinates (Rene’ Descartes)

• X (horizontal), y (vertical axis)

• Four quadrants.

• A point is located on a graph by an ordered pair of coordinates (x, y)

• Two dimensional analog of the number line.

Example: Graphing

Exercise Set 7.1 #5, 17

Plot the following points:

(-3, -5)

(3.5, 4.5)

X

Y

(0,0)

Graphing Equations

• In Chpt. 6 we looked at equations in a single variable. For linear equations the solution is typically a single value.

• Now consider an equation in two variables, solutions will be pairs, an x value and a y value.

• An equation with two variables will typically have an infinite number of solution pairs.

• We can see these solutions visually by plotting them on a graph.

• The graph of an equation is the set of all points whose coordinates satisfy the equation

Example: Graphing Equations

Exercise Set 7.1 #21, 23

Graph each equation. Select integers for x from -3 to 3.

• y = x2 – 2

• y = x - 2

Thinking Mathematically

Algebra: Graphs, Functions and Linear Systems

7.1 Graphing and Functions