MAT 109 Chapter 3 Study Guide
MAT 109 Chapter 3 Study Guide MAT 109
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This 3 page Study Guide was uploaded by Sterling Notetaker on Sunday September 4, 2016. The Study Guide belongs to MAT 109 at Barry University taught by Dr. Singh in Fall 2016. Since its upload, it has received 6 views. For similar materials see Precalculus Mathematics 1 in Mathmatics at Barry University.
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Date Created: 09/04/16
MAT 109 PreCalculus Mathematics 1 Chapter 3 Study Guide Notes L. Sterling August 27th, 2016 Abstract Give a de▯nition to each of the terms listed in this section. 1 Functions 1.1 Constant Function f(x) = b 1.2 Identity Function f(x) = x 1.3 Square Function f(x) = x 1.4 Cube Function 3 f(x) = x 1.5 Square Root Function f(x) =p x 1.6 Cube Root Function p3 f(x) = x 1.7 Reciprocal Function 1 f(x) =x 1 1.8 Absolute Value Function f(x) = jxj 1.9 Greatest Integer Function f(x) = int(x) 2 De▯nitions 2.1 Absolute Maximum When f notes a function when some interval and that there’s a number in an interval for which f(x) ▯ f(u), which would make f(u). 2.2 Absolute Minimum When a number in an interval for which f(x) ▯ f(u) for all values of x in an interval, which would make f(u). 2.3 Average Rate of Change f(b)▯f(a) Can be found in a function’s domain to be de▯ned avrA= b▯a ;a6=b = ▯x = ▯x while only when both a and b don’t equal each other. 2.4 Constant Function When it’s on an open interval, I, if, for any possible choice of just x in I when the values in f(x) are all equal. 2.5 Decreasing Function When it’s on an open interval, I, if, for any possible choice of both x and x 1 2 in I when noting that1x < 2 , which therefore notes that1f(x ) 2 f(x ). 2.6 Di▯erence Quotient f (x + h) ▯ f (; h6=0 h 2.7 Domain General sets of all of the x-coordinates, which are the ▯rst half of the elements of any ordered pair. 2.8 Even Function When every x-value in its given domain is also in their respected ▯x-values: f(▯x) = f(x) and (x;y) ! (▯x;y). 2 2.9 Function Relations between a set of inputs (x-values) and a set of outputs (y-values) 2.10 Function Notation f(x) y f Function Argument or Independent V ariable x Dependent V ariable y Function of image or x f (x) 2.11 Increasing Function When it’s on an open interval, I, if, for any possible choice o1 both 2 and x in I when noting that x < x , which therefore notes that f(x ) < f(x ). 1 2 1 2 2.12 Local Maximum Functions with one at v if there’s an I, an open interval, contains c so that, for all x-values in an I to make it f(x) ▯ f(c). 2.13 Local Minimum Functions with one at v if there’s an I, an open interval, contains c so that, for all x-values in an I to make it f(x) ▯ f(c). 2.14 Odd Function When every x-value in its given domain is also in their respected ▯x-values: f(▯x) = ▯f(x) and (x;y) ! (▯x;▯y). 2.15 Range General sets of all of the y-coordinates, which are the second half of the elements of any ordered pair. 2.16 Vertical Line Test A general set of points that are located on a xy-plane is a function’s veri▯ed graph i▯ (if and only if) every point intersects the vertical line of a graph only once. 3
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