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38 Cards in this Set
- Front
- Back
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What is the difference between natural numbers, whole numbers and integers |
Natural and whole numbers are only positive whole numbers include 0 |
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What does the inequality equation |x| < c become? |
x < c and x < -c |
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What does the inequality equation |x| > c become? |
x > c or x < -c |
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If an absolute value is less than a negative number, what is the solution? |
No solution |
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If an absolute value is greater than a negative number, what is the solution? |
All real numbers |
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What is the union symbol? |
Capital U |
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What is the conjugate? |
A binomial formed by taking the opposite of the second term of the original binomial |
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What is an even function? |
A function where f(x) = f(-x) |
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What is an odd function? |
-f(x) = f(-x) |
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What is a quadratic function? |
A equation in which the highest power an unknown is raised to is 2 |
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What affect do vertical transformations have on parent graphs? |
They cause the parent graphs to stretch or shrink vertically |
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What affect do horizontal transformations have on parent graphs? |
They cause the parent graphs to stretch or shrink horizontally |
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What affect do translations have on parent graphs? |
They cause the parent graph to shift left, right, down or up |
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What affect do reflections have on parent graphs? |
They flip the parent graph over the horizontal or vertical line |
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What causes a vertical transformation? |
The coefficient multiplying in front of a function |
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What causes a horizontal shift? |
The coefficient inside of the functions paranethisis |
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What causes a vertical shift |
Adding or subtracting numbers completely different from the function |
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What causes horizontal reflection? |
Multiplying by a negative number outside of a function |
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What causes vertical reflection? |
Multiplying by a negative number inside the function |
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What is the formula for combining multiple transformation? |
a * f[c(x -h)] + v a= vertical transform c = horizontal transform h = horizontal shift v = vertical shift |
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What are piece-wise functions? |
Functions broken into pieces depending on the input |
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What is a rational function? |
A function where the variable appears in the denominator of a fraction |
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How do you find vertical asymptotes? |
Set the denominator to 0 and solve for x. The x values will be the location of the vertical asymptotes. |
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What is the tell tell sign for a horizontal asymptote at 0? |
If the denominator has the bigger degree |
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What is the horizontal asymptote if the numerator and denominator have the same highest degree? |
It is the numerator coefficient divided by the denominators coefficient. |
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What is the tell tell sign for an oblique asymptote? |
If the numerator has a higher degree than the denominator |
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How do you find the equation for an oblique asymptote? |
Use long division of polynomials to find the quotient |
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What is a composition of functions? |
One function action upon another |
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How can you graph the inverse of a function? |
Graph the original function, then switch each x and y value to get the inverse |
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How do you find the inverse of a function? |
Switch f(x) with x Change f(x) to f^-1(x) Solve for f^-1(x) |
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How do you prove that function f and g are inverses? |
f(g(x)) = x and g(f(x)) = x |
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In a quadratic function, what is the number in front of x^2 called? |
Leading coefficient |
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In a quadratic function, what is the number in front of x called? |
Linear coefficient |
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In a quadratic function, what is the number not multiplied by an x called? |
constant |
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What is a perfect square? |
(a + b)^x |
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What is the difference of squares? |
a^2 - b^2 |
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What is (a + b)^3 |
(a + b)(a^2 -ab + b^2) |
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What is (a - b)^3 |
(a - b)(a^2 + ab + b^2) |
