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Chapter 1: Chapter 1: Functions and Functions and their Graphstheir Graphs1.1 Rectangular Coordinates and 1.1 Rectangular Coordinates and

1.2 Graphs of Equations1.2 Graphs of Equations

You know what this is already…You know what this is already…

1.1 Rectangular 1.1 Rectangular CoordinatesCoordinates

I. The Cartesian I. The Cartesian PlanePlane

IIII. The Pythagorean . The Pythagorean Theorem and the Distance Theorem and the Distance FormulaFormula

Find the distance Find the distance between (2, -5) and (8, between (2, -5) and (8, 3).3).

Show that the points (1, Show that the points (1, -3), (3, 2), and (-2, 4) -3), (3, 2), and (-2, 4) form an isosceles form an isosceles triangle. triangle.

The midpoint between two generic points The midpoint between two generic points can be found by taking the average of the x-can be found by taking the average of the x-coordinates and the average of the y-coordinates and the average of the y-coordinates…coordinates…

Find the midpoint of the line segment Find the midpoint of the line segment joining the points (-9, 5) and (4, 2)joining the points (-9, 5) and (4, 2)

III. The Midpoint III. The Midpoint FormulaFormula

““A A solutionsolution of an equation in two variables (x and of an equation in two variables (x and y) is an ordered pair (call it (a, b) ) such that when y) is an ordered pair (call it (a, b) ) such that when x is replaced with a and y replaced by b, the x is replaced with a and y replaced by b, the resulting equation is a true statement….”resulting equation is a true statement….”

WHAT? Basically, if the point fits into the equation, WHAT? Basically, if the point fits into the equation, then that point should be included in the graph of then that point should be included in the graph of the equation. the equation.

The actual graph is the set of ALL points that work. The actual graph is the set of ALL points that work.

1.2 Graphs of Equations1.2 Graphs of EquationsI. The Graph of an I. The Graph of an EquationEquation

Sketch the graph of the following:Sketch the graph of the following: y= 2x+1y= 2x+1

WHEN IN DOUBT PLOT WHEN IN DOUBT PLOT (KINDA) RANDOM POINTS(KINDA) RANDOM POINTS

WHEN IN DOUBT PLOT WHEN IN DOUBT PLOT (KINDA) RANDOM POINTS(KINDA) RANDOM POINTS

X- InterceptX- Intercept

Y-interceptY-intercept

How do you find them?How do you find them?

II. Intercepts of a II. Intercepts of a GraphGraph

Find the x and y Find the x and y intercept of:intercept of:

III. SymmetryIII. Symmetry

A circle with a center (h, k) and a radius r A circle with a center (h, k) and a radius r consists of all points (x, y) equidistant from consists of all points (x, y) equidistant from the center. We can find the equation of a the center. We can find the equation of a circle from what we know of the distance circle from what we know of the distance formula…formula…

Find the standard form of the equation of a Find the standard form of the equation of a circle with center at (2, -5) and a radius of 4. circle with center at (2, -5) and a radius of 4.

IV. CirclesIV. Circles