Math Class Notes

Class 1:

Circle function: (x-h)2+(y-v)2=r2

• canter radius/standard form

• “h” and “v” represent the center of the circle (h,v)

• If there are no “h” and “v”s, then the center point is simply at (0,0) and can be thought of as “(x-0)2+(y-0)2”

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To find whether a point is on, inside or outside the circle, just insert it into the question and compare it to the previous one of the circle you want to determine its relationship with.

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Find the vertex of the parabola by using the negative of the term with “x” and the term after the bracket with “x”.

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*Note: Function - one independent can only have one dependant variable (use vertical line test)

The dependant variable is the first one in the pair

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The difference between relation and function is that function can only have one secondary number

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Domain is all the independent variables (x)

Range is the dependant variables (y)

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• Two main ways to represent a function. One is a graph and the other is pairs (table works too)

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Square root function

Reciprocal function

Absolute value function

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Class 2:

• Usually graph three points but for quadratic it has to be at least 5
• VA = vertical asymptote = the number x is being subtracted/added by (absolute value)
• HA = horizontal asymptote = the other number outside of the x interaction

Don't touch the asymptotes

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How to find…

Domain: within the square root, is greater or equal to 0

Range: the number outside of the square root

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Transfer:

1. Always do negative first (reflect over x-axis if negative)
2. Vertical stretch by factor of the number before the square root (absolute value)
3. Horizontally compressed by factor of 1/(number within the square root but outside the x bracket) 
4. Translate right/left *number beside x in bracket* and up/down *number outside of square root*

#Note: 

X-axis - negative = right, positive = left

Y-axis - positive = up, negative = down

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