Coordinates and Graphsin the Plane

Coordinate Plane

x-axis

y-axis

origin

Quadrants

x

y

III

III IV

Scale

x

y

P(x, y)P(3, 2)

Ordered Pairs

x

y

Directions

x

y

(+, +)(–, +)

(–, –) (+, –)

Finite Intervals

Set of all real numbers that lie strictly between two fixed numbers a and b a and b: “endpoints” open interval: endpoints not

included a < x < b (a, b) on the number line:a b

Finite Intervals

Set of all real numbers that lie between and include two fixed numbers a and b closed interval: endpoints included a ≤ x ≤ b [a, b] on the number line:

a b

Finite Intervals

An interval containing only one endpoint half-open interval a < x ≤ b OR a ≤ x < b (a, b] OR [a, b) on the number line:

a b a b

Infinite Intervals

All Real Numbers the complete number line –∞< x <∞ (–∞, ∞) on the number line:

Infinite Intervals

Set of numbers greater than a x >a (a, ∞) on the number line:

a

Infinite Intervals

Set of numbers greater than or equal to a x ≥a [a, ∞) on the number line:

a

Infinite Intervals

Set of numbers less than b x <b (–∞, b) on the number line:

b

Infinite Intervals

Set of numbers less than or equal to b x ≤b (–∞, b] on the number line:

b

A Viewing Windowon the Coordinate Plane

Points in the coordinate plane that correspond to a set of ordered pairs is a graph of the set.

The graph represents a small portion of the coordinate plane. “Viewing Window” or “View”

Graphs by Hand

Make a table of xy-pairs that fit the equation

Sketch coordinate axes with scales that will fit the points in your table

Plot the points (x, y) from the table Sketch a smooth curve through the

plotted points Label the curve with its equation

Graphs on TI Calculators

Select the Y= screen and enter the equation on one of the available lines

Set the dimensions of the viewing window using WINDOW or ZOOM

Select the GRAPH screen Mode

connected vs. dot sequential vs. simultaneous

Intercepts Algebraically

Intercepts The points where a graph touches

or crosses an axis X-Intercept

Set y=0 in the equation and solve for x

Y-Intercept Set x=0 in the equation and solve

for y

Intercepts Graphically

Use graphing calculator to graph the equation Can be inaccurate

X-Intercept 2nd Calc 2:zero

Y-Intercept TRACE 0 ENTER