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### 23 Cards in this Set

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 Define a function a rule which takes certain numbers as inputs and assigns to each input exactly one output number Could the following points be points of a function? (1,1), (2,4), (0,0), (2,5) (1,9) No, the input of one has two output values- 9 and 1. The input of 2 has two output values- 4 and 5. What does the vertical line test tell us about a graph? If there is a vertical line that intersects a graph in more than one point, then the graph is NOT a function. Let P=f(x). What is the independent variable? What is the dependent variable? independent=x dependent=P Explain what is meant by the symbol g(3) g(3) is the output of the function g when its input is 3 write the following relationship in function notation: number of molecules, m, in a gas, is a function of the volume of the gas, v. m=g(v) The sales tax on an item is 6%. Express the total cost, C, in terms of the price of the item, P C(P)=P + 0.06*P Let S(f) represent the number of frogs in a bog of surface area f. What does S(4)=20 mean? S(4)=20 means that a bog of surface area 4 has 20 frogs in it. for the point (a,b) what is the input and what is the output? a=input b=output If given a table with x values: 1,2,3,4,5 and Y values: 6,12,18,24,30 Then to prove it is a linear function you need to..... Show that the slope remains the same along all intervals. Must check all intervals What is the formula for the slope of a line? slope=(change in y)/(change in x) The graph of the equation y=k is a __________ with a slope that is ________ horizontal, 0 the graph of the equation x=k is a ____________ with a slope that is __________ vertical line, undefined if m1 and m2 are the slopes of lines that are perpendicular to one another, then how are m1 and m2 related? m1=-1/m2 i.e. m1 is the opposite recipricol of m2 and vice versa If l1 and l2 are parallel lines then their slopes are.... equal if Q=f(t) then Q is an increasing function if __________, and Q is decreasing if___________. the values of f increase as the values of t increase when the graph is read left to right. the values of f decrease as the values of t increase when the graph is read left to right. If Q=f(t), then if f is an increasing function what can be said about its average rate of change on every interval? What if f is a decreasing function? increasing- the average rate of change(slope) is positive on every interval decreasing- the av rate of change(slope) is negative on every interval. True or false, [f(b)-f(a)]/[b-a] is the average rate of change over the interval a<=t<=b True, f(b)-f(a) is simply change in y b-a is simply the change in x What is the general formula for a linear function and what does each term represent? y=b+mx b=y intercept (where x=0) m=slope of the line True or false there are some instances where the graph of a linear function is not a straight line false, the graph of a linear function is always a straight line If you are given the points (1,2) and (4,7) what is the equation of the line that passes thru these points? m= (2-7)/(1-4)= -5/-3 = 5/3 y=b+(5/3)x 2=b+5/3 b=2/6=1/3 y=1/3+(5/3)x What are the slope intercept, point-slope and standard form of a linear function? slope-intercept: y=b+mx point-slope: y-y0=m(x-x0) where (x0, y0) is a point on the line standard form: Ax +By +C=0 Where do the lines y=9x+1 and g=-2x intersect? to find intersection points of two graphs, set them equal to eachother and solve for x: 9x+1=-2x 11x=-1 x=-1/11 since x=-1/11, then -2(-1/11)=2/11 gives the y value so the graphs intersect at (-1/11,2/11)