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STAT week 6

by: Carrie Notetaker

STAT week 6 STAT 1001 - 702

Carrie Notetaker

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Introduction of Functions: linear and quadratic
Class Notes
Math, Statistics, Calculus, Precalculus, functions
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This 2 page Class Notes was uploaded by Carrie Notetaker on Thursday October 6, 2016. The Class Notes belongs to STAT 1001 - 702 at Temple University taught by Kapanjie in Fall 2016. Since its upload, it has received 4 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS I in Business at Temple University.

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Date Created: 10/06/16
STAT 10/04 Functions y= f (x) 1. ; to solve substitute the value of x into the function and solve  remember to write the answer as an ordered pair ex: (-3,2)  whenever you find f (0) you are always going to be left with just the constant 2. f (x+h) ; to solve substitute x+h into the function  remember to foil the (x+h ) 3. Domain: the set of input values for which the function is defined  Racial functions: denominator cannot equal zero  Radical functions: cannot take the square root of a negative number  To find the domain of a racial functions, set the denominator equal to zero to find the values that x cannot be  To find the domain of a radical functions, focus on the radical and find the values that x cannot be f(x+h )− f(x) 4. Difference quotient: h  To find the difference quotient: 2 2 (a) Find f (x+h) first: x +2 xh+h (b) Do the whole nominator: f (x+h)– f (x) (c) Combine like-terms (d) Do the whole quotient using the previous solutions 5. Business application  Place function in calculator and find the x value for said question  Can be used to estimate stock flow Applications of linear functions c(x =mx+b 6. Cost= m: marginal cost b: fixed cost C x C x = ( 0 7. Average cost= ( 0 x0  To solve for average cost, you divide the cost by the number of units 8. Revenue= R(x)=px p: selling price 9. Profit= P (x=R(x)−C(x) 10.Linear Depreciation function: use the two ordered pairs to find the equation of the line (find slope and y-intercept)  To solve the function, you substitute the value in for x and solve 11.Supply and Demand: use the linear equation to find the value for demand or supply, make sure you use the right equation  Don’t be afraid to use your calculator for graphs and equation solving  Y-max on calculator should always be the y-intercept of the demand function  To find equilibrium, select the ordered pair (quantity, price) where the two graphs intersect (supply=demand) Quadratic Functions 2 12. y=a x +bx+c  X-intercept: when the graph crosses the x-axis (x,0)  Y-intercept: when the graph crosses the y-axis (0,y)  Vertex: lowest or highest point of the graph (max or min)  a>0: parabola shaped like a U a<0: parabola shaped like ꓵ y=f −b ,x= −b 13.vertex: (2a 2a y=0 14.x-intercept: set 15.y-intercept: set x=0 or just the c value 16.axis of symmetry: middle of parabola, x value of the vertex 17.Revenue function: same as linear functions, remember to distribute the x  Max and min have to do with the vertex of the parabola  When finding the actual max or min revenue, plug the value into the revenue function 18.Supply and Demand: same as linear functions, remember to find the calculator window when graphing  Price is your y when it comes to supply


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