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urp:algebra
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urp:algebra [2021-11-08] nerf_herder [Functions] |
urp:algebra [2021-11-08] nerf_herder |
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| ====Algebra & Pre-Calc==== | ====Algebra & Pre-Calc==== | ||
| + | Related pages: | ||
| * [[Graphing|Graphing circles, ellipses, parabolas, hyperbolas]] | * [[Graphing|Graphing circles, ellipses, parabolas, hyperbolas]] | ||
| * [[poly|Polynomials, quadratic formula and completing the square]] | * [[poly|Polynomials, quadratic formula and completing the square]] | ||
| Line 6: | Line 6: | ||
| **quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | **quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | ||
| - | **PEMBAS/BODMAS ** - order of operations: Parentheses (brackets), exponents (order), multiply/divide, add/subtract | + | **PEMDAS/BODMAS ** - order of operations: Parentheses/Brackets, Exponents/Order, Multiply-Divide, Add-Subtract |
| ==== System of equations==== | ==== System of equations==== | ||
| Line 63: | Line 63: | ||
| ==== 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 | ||
| Line 89: | Line 89: | ||
| 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 a 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:** | ||
urp/algebra.txt · Last modified: 2022-02-01 by nerf_herder
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