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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)]/[ba] is the average rate of change over the interval a<=t<=b 
True, f(b)f(a) is simply change in y
ba 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= (27)/(14)= 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, pointslope and standard form of a linear function?

slopeintercept: y=b+mx
pointslope: yy0=m(xx0) 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) 