Coordinates and Graphs in the Plane. Coordinate Plane x-axis y-axis origin.

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Presentation transcript:

Coordinates and Graphs in the Plane

Coordinate Plane x-axis y-axis origin

Quadrants x y I II 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 ba 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 Window on 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 2 nd Calc 2:zero Y-Intercept TRACE 0 ENTER