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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)