Pre Calc 1 - Notes taken by student for precalc lecture. PDF

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Notes taken by student for first half of precalc practice. ...

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Intersection with the axis:

! ! ! ! ! ! ! ! ! Get e as a function of x Express y as a function of x

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Why does this work?

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How do we get a graph of the function?

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! ! ! ! ! ! ! ! ! What is a normal Vector of e? (Length isn't imp) ! An arbitrary vector perpendicular to the line (e) ! ! ! ! ! ! ! ! ! ! ! Directional Vector of e? ! An arbitrary vector parallel to the line e ! " " OR! ! ! ! ! ! ! ! ! ! We could get the vector with a value of lamda ! or if we have two points on the line. ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! How to get a normal vector? ! How to rotate a vector by 90°

Switch x and y coordinates and multiply by -1 (x, y) . (-y,x) = -xy +xy = 0 With the scalar/dot product, when it = 0 the vectors are perpendicular

It works because it's like we're rotating the axis

What is the gradient or slope of a line? How do we define a gradient? Gradient of e? What does the grad. tell us? The coefficient x. For every 1 unit in x it travels 2 units downwards or upwards if positive. tangent function...