Cartesian coordinate system

the geometric or graphical representation of a relation and/or

function

OR without geometry, algebra is pointless!

The first person to describe coordinates was Pierre de Fermatin a book of math investigations around 1629 but was not published until about 1679.

But the system we know today bears its’ name from a man named Rene Descartes

His modern version of (x,y) ordered pairs or coordinates known as the

Cartesian coordinate system

that uses axes to find the distance of a given point from an origin (0,0) was written about 1637.

The horizontal axis is also known as the x – axis and is used to plot the cause, input or independent quantity.

The vertical

axis is also known as the y – axis and is used to plot the effect, output or dependent quantity.

The modern coordinate system graphs the relation between two quantities as points or a set of points.

Remember ‘C’:Quadrant ICoordinates are (+,+)

The origin (0,0)

Quadrant IICoordinates are (-,+)

Quadrant IIICoordinates are (-,-)

Quadrant IVCoordinates are (+,-)

Location of a point is given by an ordered pair with coordinates.

Ex. (x, y) or (x, f(x))

The domain is all the x values that make sense for a particular relation.

It can be continuous, in which every quantity between all the graphed x values makes sense.

D: { 0 < x < ∞ }

time (working)

In this case time is continuous—all values between 0 and ? (however long you work) make sense.

The domain can also be discrete. It might have values between each point that do not make sense.

Ex. D: {0, 1, 2, 3, 4}

number of pets owned

num

ber o

f stu

dent

s Would all the values between each point make sense?Could a student own half a pet?

The range is all the permissible y values . Ex. R: {1, 2, 6, 24}

Let’s consider the relation in the song you hear…..

time (working hours)

time

(off

hour

s)

The maximum value (high point) for time off is 24 hours.

The minimum (low point) hours off is 0.

As x values of ‘time working’ increase, the y values of ‘time off’ decrease,

so it is a decreasing function.

The domain, or working hours, is

continuousfrom 0 as all values from 0 make sense.

So time is love…..someone who waits for your time off may surprise you!

Cartesian coordinate system

A. Murray 2012