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Formulas to Know

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  • Slope

    m = Y2 - Y1

    X2 - X1

  • Point Slope

    y - y1 = m ( x - x1 )

  • General Standard Equation

    Ax + Bx = C

  • General Form

    Ax + Bx +C = 0

  • Order of Transformation

    1. Horizontal Shifts

    2. Stretches and Compressions

    3. Reflections

    4. Vertical Shifts

  • Sum : ( f + g )(x)

    f(x) + g(x)

  • Difference : ( f - g )(x)

    f(x) - g(x)

  • Product : (fg)(x)

    f(x) \(\cdot\)g(x)

  • Quotient : \(\left(\frac{f}{g}\right)\left(x\right)\)

    \(\frac{f\left(x\right)}{g\left(x\right)}\)

  • Function Composition \(\left(f\omicron g\right)\left(x\right)\)

    f composed with g of x

    f(g(x))

  • How to find \(f^{-1}\left(x\right)\)

    1. Replace X with Y

    2. Interchange x and y

    3. solve for y

    4. replace y with \(f^{-1}\left(x\right)\)

  • One - One Functions

    Pass Horizontal and Vertical line tests

  • Pythagorm Thearm

    \(a^2+b^2=c^2\)

  • Distance Formula

    \(d=\sqrt{\left(x2-x1\right)^2+\left(y2-y1\right)^2}\)

  • Midpoint Formula

    \(\left(\frac{x1+x2}{2},\frac{y1+y2}{2}\right)\)

  • Area of a Circle

    \(\pi r^2\)

  • Circumfrance of Circle

    \(2\pi r\)

  • Diameter

    \(\pi\)