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Transformations: Add 4 in parenthases |
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Transformations: Subtract 8 in parenthases |
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Transformations: Subtract 8 outside parenthases |
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Transformations: Add 6 outside parenthases |
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Transformations: Multiply 4 outside parenthases |
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Vertical Stretch by a factor of 4 |
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Transformations: Multiply 4 inside parenthases |
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Horizontal compression by factor of 4 |
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Transformations: Multiply 1/2 inside parenthases |
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Horizontal stretch by factor of 2 |
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Transformations: Negative inside parenthases |
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Transformations: Negative outside parenthases |
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Graphing rationals: Vertical Asymptotes |
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Definition
Simplify the factored rational expression. Set any remaining factors of the denominator equal to zero. A vertical asymptote will occur at each of these x-valus. |
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Graphing rationals: Horizontal Asymptotes |
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Definition
The leading coefficent of the numerator over the leading coefficent of the denominator |
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Graphing rationals: Holes |
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Find the zero of the part of the equation that cancels's out |
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Graphing rationals: Domain |
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Definition
Set each factor of the denominator equal to zero. This is where the function will be undefined. The domain for the function will be all real numbers except those that make the denominator zero. |
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Graphing rationals: x-intercepts |
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Set numerator to zero/set y to zero |
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functions: When exponent is even |
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functions: When exponent is odd |
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functions: When leading coefficent is negative even |
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left: negative infinity right: negative infinity |
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functions: When leading coefficent is negative odd |
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left: positive infinity right: negative infinity |
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functions: When leading coefficent is positive odd |
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Definition
left: negative infinity right: positive infinity |
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Matrices: row's by colums or colums by rows? |
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matrices: can matrices be added or subtracted if different dimensions? |
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matrices: which matrix determines row when multiplying? |
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Matrices: how do you solve a system with matrices |
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First divide up the system into 2 matrices. The coefficent matrix and the constant matrix. Then multiply the inverse of the coefficent matrix by the constant matrix. |
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Matrices: what are the dimensions of a product matrix |
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The rows of matrix A and the colums of matrix 2 |
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Matrices: when can you not multiply matrices |
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Definition
When the columns of matrix A is different than the rows of matrix B |
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Matrices: how do you find the inverse of a matrix |
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Definition
Figure out what you must multiply the matrix by to get to get the indentity matrix |
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Matrices: what is the identity matrix |
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In a square matrix it is when ther are ones going down the middle line on a - slope (1,0/0,1) |
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