1.1 Functions and their Graphs

Pre Calc PHSP

The rectangular coordinate system (Cartesian plane)

you can represent ordered pairs of real numbers by points on this

x-axis

The horizontal real number line

y-axis

the vertical real number line

origin

The point of intersection of these two axes

quadrants

the two axes divide the plane into four

ordered pair

(x,y)

𝑥-coordinate represents the directed distance from the

𝑦-axis to the point (left and right)

𝑦-coordinate represents the directed distance from the

𝑥-axis to the point (up and down)

The pythagorean Theorem

a² + b² = c²

The distance formula

d = sqrt (x₂ - x₁)² + (y₂ - y₁)²

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">

<mrow>

<mi>d</mi>

<mo>=</mo>

<msqrt>

<mrow>

<msup>

<mrow>

<mrow>

<mo>(</mo>

<mrow>

<msub>

<mi>x</mi>

<mn>2</mn>

</msub>

<mo>-</mo>

<msub>

<mi>x</mi>

<mn>1</mn>

</msub>

</mrow>

<mo>)</mo>

</mrow>

</mrow>

<mn>2</mn>

</msup>

<mo>+</mo>

<msup>

<mrow>

<mrow>

<mo>(</mo>

<mrow>

<msub>

<mi>y</mi>

<mn>2</mn>

</msub>

<mo>-</mo>

<msub>

<mi>y</mi>

<mn>1</mn>

</msub>

</mrow>

<mo>)</mo>

</mrow>

</mrow>

<mn>2</mn>

</msup>

</mrow>

</msqrt>

<mo>.</mo>

</mrow>

</math>

Midpoint Formula

m = (x₁ + x₂/2 , y₁ + y₂/s)