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Math 251 – Week 0 Activity

Thursday, September 22

1) We will start off by reviewing the concept of function.

a) What is your definition of function? (in your own words)

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

your calculator.)

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

…

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