Calc
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Relation | a pairing of elements of one set with elements of a second set. This is usually expressed as a set of ordered pairs.
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| Domain | the set of all abscissas (the first value in the ordered pair) of the ordered pairs.
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| Range | the set of all ordinates (the second value in the ordered pair) of the ordered pairs.
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| Function | this is a relation in which each element of the domain is paired with exactly one element in the range.
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| Function Notation | The symbol f(x) is read “f of x”. f(x) = y, therefore the ordered pairs of a relation are in the form (x, y) or (x, f(x)).
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| Vertical Line Test | If every vertical line drawn on the graph of a relation passes through no more than one point on the graph, then the relation is a function.
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| Excluded values | real numbers when substituted in for “x” will give an imaginary number for “y” or be undefined.
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| Composition of Functions | Given functions f and g, the composite function f ◦ g can be described by the following equation: [f ◦ g](x) = f(g(x))
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| Iteration | The composition of a function to itself.
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| Inverse functions | Two functions f and g are this iff [f ◦ g](x) = [g ◦ f](x) = x.
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| Property of Inverse Functions | Suppose f and f1 are this. Then, f(x) = y iff f-1 (y) = x.
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| Linear Equation | This has the form Ax + By = C, where A and B are both not zero. The graph is always a line.
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| Solution of a Linear Equation | An ordered pair that makes the equation true. Each ordered pair corresponds to a point in the coordinate plane.
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| Linear Function | This is defined by f(x) = mx + b, where m and b are real numbers.
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| Zeros of the Function f | values of x for which f(x) = 0. (These are the x-intercepts.)
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| X-intercept | The point at which a graph crosses the x-axis. In a linear function, this will have coordinates
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| Constant Function | A function f is this if f(x) = b. The graph is a horizontal line. This either has no zeros (b ≠ 0)or every value of x is a zero (b = 0).
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| Linear Inequality | This has the form Ax + By + C < 0, Ax + By > C, Ax + By > C, or Ax + By < C, where A and
B are both not zero. The graph consists of a boundary and the shading of a region.
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| Pythagorean Theorem | In a right triangle, the sum of the squares of each leg equals the square of the hypotenuse.
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| Slope-Intercept Form | This form of an equation of a line is y = mx + b. The slope is m and y-intercept is b.
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| y-intercept | The point where the graph crosses the y-axis.
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| Point-Slope Form | If the point with coordinates (x1, y1) lies on a line having slope m, this form of the equation of the line can be written as follows.
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