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urp:algebra [2021-11-08] nerf_herder [Functions] |
urp:algebra [2021-11-08] nerf_herder |
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**quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | **quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | ||
+ | |||
+ | **PEMDAS/BODMAS ** - order of operations: Parentheses/Brackets, Exponents/Order, Multiply-Divide, Add-Subtract | ||
==== System of equations==== | ==== System of equations==== | ||
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==== Logs ==== | ==== Logs ==== | ||
- | inverse of a power | + | Log is the inverse of a power |
x = bᵉ, e = logᵦ(x) (b = base, 10 by default) | x = bᵉ, e = logᵦ(x) (b = base, 10 by default) | ||
eg. 2³ = 8, log₂(8) = 3 | eg. 2³ = 8, log₂(8) = 3 | ||
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composition of functions: (f’g)(x) = f(g(x)), order of evaluation is important | composition of functions: (f’g)(x) = f(g(x)), order of evaluation is important | ||
- | inverse of function - only possible if no two values of x produce the same result | + | **Inverse** of a function - only possible if no two values of x produce the same result, ie. must be one-to-one (or limit the domain to make it so) |
Example: To find f⁻¹(x) for f(x) = 5x + 3 | Example: To find f⁻¹(x) for f(x) = 5x + 3 | ||
y = 5x + 3 | y = 5x + 3 | ||
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since x is input to the function, and y is output) | since x is input to the function, and y is output) | ||
- | graphing an inverse: reflection of the graph about the line y=x | + | Graphing an inverse: reflection of the graph about the line y=x |
**horizontal and vertical asymptotes:** | **horizontal and vertical asymptotes:** |