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23 Cards in this Set

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  • Back
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?
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.
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?
If given a table with x values:

and Y values:

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?

i.e. m1 is the opposite recipricol of m2 and vice versa
If l1 and l2 are parallel lines then their slopes are....
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,


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?

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
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:

since x=-1/11, then -2(-1/11)=2/11 gives the y value so the graphs intersect at (-1/11,2/11)