Math 103 College Algebra – Flashcards
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Natural numbers
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counting numbers does not include 0.
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Integers
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..., -3, -2, -1, 0, 1, 2, 3, ...
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Rational numbers
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includes 0, integers, fractions, repeating and terminating decimals
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Irrational numbers
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non-repeating, non-terminating decimals, ∏ (pi?), √2, √-5, ³√7
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Real numbers
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any number on the number line includes rational and irrational
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158,000 in scientific notation
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1.58 x 10⁵
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Steps to standard equation of a circle
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Take endpoints, find the center (midpoint formula), then find the radius (distance formula).
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relation
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a set of ordered pairs
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domain
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the set of x values in a relation
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range
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the set of y values in a relation
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function
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a relation in which each element in the domain corresponds to exactly one element in the range.
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{ x '|' 1 ≤ x ≤ 5 }
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set-builder notation the set of all real numbers such that x is greater than or equal to 1, and less than or equal to 5.
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Vertical line test
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If every vertical line intersects a graph at no more than one point, then the graph represents a function.
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What is the domain of f(x) = 1/√x+4
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{ x | x > -4 }
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Constant function
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f(x) = b
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Linear function
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f(x) = ax + b
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∪
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union, means "or"
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∩
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means "and"
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Interval Notation:|(-2, 2)
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-2 < x < 2
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Interval Notation:|(-1, 3]
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-1 < x ≤ 3
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Interval Notation:|[-3, 2]
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-3 ≤ x ≤ 2
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Interval Notation:|(-3, ∞)
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x > -3
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Interval Notation:|(-∞, 1]
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x ≤ 1
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Interval Notation:|(-∞, -2] ∪ (1, ∞)
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x ≤ -2 or x > 1
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Square the binomial (t + h)²
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(t² + 2th + h²)
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Factor out the h 4th +2h² / h
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= h(4t + 2h) / h (remove the h's) = 4t + 2h
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³√8
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Cube root ³√8 = 2 (2 x 2 x 2 = 8)
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model
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A good model describes and explains current data. It should also make predictions and forecast phenomena. (2.1)
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interpolation
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estimating values between data points; more accurate than extrapolation. (2.1)
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extrapolation
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estimating values "outside" of the given data points; less accurate than interpolation. (2.1)
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domain of a model
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must have limits, i.e. D = 0, 1, 2, or 3. (2.1)
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y-intercept
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b of the function f(x) = ax + b; the point where a line intersects with the y axis. (2.1)
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x-intercept
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the point where a line intersects with the x axis; aka zero of f. (2.1)
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slope
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a of the function (f(x) = ax + b; indicates the number of units on the y axis a line rises or falls for every one unit on the x axis. (1.4)
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Modeling with a Linear Function
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f(x) = (constant rate of change)x + (initial amount)
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approximate linear data
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1. find the slope (a) between data sets using slope formula. 2. determine the y-intercept (b). 3. use f(x) = ax + b function.
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constant function
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A function f represented by f(x) = b, where b is a constant (fixed number), is a constant function. (1.4)
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linear function
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a function f represented by f(x) = ax + b, where a and b are constants, is a linear function.
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rise / run
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slope
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what is the slope of f(x) = -½x + 5?
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-½
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what is the y-intercept of f(x) = -½x + 5?
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5
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the slope is aka
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average rate of change
