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Math 251 – Week 0 Activity
Thursday, September 22
1) We will start off by reviewing the concept of function.
b) What is your definition of the domain of a function? (in your own words)
c) What is your definition of the range of a function? (in your own words)
d) What are some important features of a function that we can identify from its graph?
Math 251 – Week 0 Activity
Thursday, September 22
2) Using your definition of a function, or the definition decided on by the class, identify which of the
following relations are functions, and explain why each is or is not. If the relation is a function, identify
its domain and range.
a)
=
, where
is the input and
is the output
b)
c)
d)
( )
-5
-4
-3
-2
-1
0
1
2
3
3
2
3
2
3
2
3
2
3
e) Taking students in this class as the set of inputs, and outputting each student’s birth mother.
Math 251 – Week 0 Activity
Thursday, September 22
3. A function that models the volume of a box is a polynomial given as
( ) = (8.5 − 2 )(11 − 2 ).
a. Often times when we encounter polynomials, they are in standard form,
an x n + … + a1 x + a0 . Give the formula for V from problem 1 in standard form.
b. What is the degree of V? ______________
c. What is the leading coefficient of V? ________________
4. The graph of V is given (label each axis, include units).
a. On what interval(s) is V increasing?
_________________________________
b. On what interval(s) is V decreasing?
_________________________________
c. Estimate any local maxima of V, and identify
where those occur.
d. Estimate any local minima of V, and identify
where those occur.
Math 251 – Week 0 Activity
Thursday, September 22
5. Consider the rational function f ( x) 
3 x2  3 x  6 3( x  2)( x + 1)

.
2 x2  4 x  16 2( x  4)( x + 2)
a. For what values of x will the numerator of f ( x) be zero?
b. For what values of x will the denominator of f ( x) be zero?
c. What is the domain of f ?
d. Identify any vertical asymptotes of f .
e. Identify the x and y intercepts of the graph of f .
Math 251 – Week 0 Activity
Thursday, September 22
6. Now we will turn our attention towards horizontal asymptotes. Horizontal asymptotes can
describe the end behavior of rational functions. Not all rational functions have a horizontal
asymptote. Decide if each of the following has a horizontal asymptote or if it will blow
up/down to +/- infinity. If the function has a horizontal asymptote, give its equation.
a.
f ( x) 
x +1
3x + 5 x  2
2
Explain how to determine if a rational function
has each of the following when looking at its
formula.
– A horizontal asymptote of y = 0.
– A horizontal asymptote other than y = 0.
b. g (t ) 
3t 2 + 5t  2
t +1
– No horizontal asymptote.
c. h( x ) 
5 x3  3 x 2 + 1
2 x3 + 4
Math 251 – Week 0 Activity
Thursday, September 22
7. The formulas for two exponential functions are given below.
( )=8
( )= 2∙3
a. Determine each of the following:
(1) =
(0) =
(−2) =
=
b. What is the domain of f? What is the domain of g?
c. Complete the tables below by looking for a pattern in the given values. (Try not to use
x
( )
-4
1
2
=8
x
( ) = 2∙3
-3
-2
128
-4
2
81
-3
-2
-1
0
1
16
8
4
-1
2
3
0
1
2
6
2
3
4
1
2
2
3
4
d. Use the tables of values above to label the graphs below as f or g.
e. Label the y-intercept on each of the graphs. How is the y-intercept related to the
function formula?
162