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Calc Cheat sheet Function One input of y cannot have more than 1 input of x X is the independent variable, It is a variable that stands alone and isn't changed by the other variables you are trying to measure. Y is the dependant variable, It is something that depends on other factors Explicit form A variable expressed as another variable ? = 3 ? 2 + 2, the variable y is explicitly written as a function of x. implicitly cos( ?? )= ?? + sin( ? ), is defined implicitly, there is no method to solve for y and express the function explicitly. Difference quotient Tells the slope of the secant line that passes through two points of the curve measure of the average rate of change of the function over an interval (in this case, an interval of length h) Simplifying expression to cancel out h 1. Factoring technique 2. Rationalize Number technique 3. Common denominator technique Piece wise function When a function is defined by different equations on different parts of its domain, it is called a piecewise- defined function
Even and Odd functions Even functions For an even function: for every point ( ? , ? ) on the graph, the point (− ? , ? ) is also, on the graph f(x) = f(-x). Symmetry on the y axis Odd functions For every point ( ? , ? ) on the graph, the point (− ? , − ? ) is also on the graph. Odd functions have origin Symmetry
Increasing, decreasing and constant functions
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