Math 1118 - Exam 2 - topics

Covering Sections  2.5-2.8, 3.1 - 3.3, 3.6, & Supplements

 

This is not necessarily a comprehensive list but it may remind you of topics you have forgotten.

Be able to:

 

1.                  Find the coordinates of the relative maximum and relative minimum of function either using your calculator or algebraically (a quadratic).

2.                  Express one quantity as a function of another quantity. i.e. express the area of a circle as a function of the diameter.

3.                  Model and solve application problems.

4.                  Find the sum, difference, product, quotient, or composition of two functions, given the function rule, a graph, or a set of ordered pairs describing each function.

5.                  Find the domain of a function, the sum, difference, product, quotient, or composition of two functions.

6.                  Model problem situations (sections 2.6 & 2.7)

7.                  Find the maximum or minimum value of a quadratic function both analytically and graphically.

8.                  Determine whether or not a function is one-to-one.

9.                  Describe the relationship between the graph of a function and its inverse.

10.              Find the inverse of a function if you are given the function rule, the graph of the function, or the set of ordered pairs describing the function.

11.              Sketch the graph of any polynomial function (assuming you can factor it) without the use of your calculator using  &  intercepts and tail behavior.

12.              Find approximate zeros of a polynomial using the graph.

13.              Find the equation of a polynomial function given the zeros of the polynomial.

14.              Understand the relationship between the zeros of a polynomial , the -intercepts of the graph of a polynomial , and the solutions (roots) to the equation , and the factors of the polynomial .

15.              Use the Remainder and Factor Theorem.

16.              Find the exact value of all zeros of a polynomial function (when possible).

17.              Find vertical and horizontal asymptotes of a function.

18.              Graph Rational Functions.

19.              Descartes’ rule of signs.

 

Math 1118

Review Test 2

 

1.                  Find the maxima and minima of the following problems:

      a.        

      b.                    

      c.        

2.                  Find the equation of the parabola with a vertex at (-2, 3) and passing through the point (1, 8).

3.                  A ball is thrown across a playing field.  It’s path is determined by where x is the distance traveled horizontally and y is the height of the ball in feet.

a.                   What is the ball’s maximum height?

b.                  How far will the ball travel before it hits the ground?

4.                  A person travels from point A to a point B, seven miles downstream and on the opposite side of a straight river.  The river is 1 mile wide.  To do this he is going to swim to a point X miles from point B on the opposite side and then run from there to point B.  He swims at 2.2 mph and runs at 7.5 miles per hour.  Find the point X where he should swim to in order to minimize the time it will take to get from point A to point B.

5.                  Jessica is making a box from a rectangular piece of cardboard by cutting squares out of each corner and folding up the sides.  The piece of cardboard is 18 inches by 24 inches.  What size squares, to the nearest tenth of an inch, should she cut out to maximize the volume of the box?  What will the volume be to the nearest tenth of a cubic inch?

6.                  Rob is making boxes with a square base such that the volume of the box needs to be 1000 cubic centimeters.  The cost of the bottom of the box is 10cents per square centimeter and the cost of the sides is 4 cents per square centimeter.  Find the dimensions of the box that minimize the costs.

7.                  Let, , and .  Find the following and their domains.

a.                   (f + g)(x)

b.                  (f/g)(x)

c.                   g(h(x))

d.                 

e.                  

8.                  The volume of a spherical balloon is increasing at 10 cc/sec.

a.                   Find a function, f, that models the volume of the balloon with respect to time.

b.                  Find a function, g, that models the radius as a function of the volume.

c.                   Find and what does this represent?

 

 

9.                  Given the graph below, find f-g where f is the top function and g is the bottom function. 

 

10.              If a function is 1-1 does it always have an inverse function?

11.              If a function has an inverse function, must it be a 1-1 function?

12.              If a function f(x) has a domain x > 2 and a range y < 3 what are the domain and range of ?

13.              Determine the inverse functions of the following.  If the do not have an inverse function, limit the domain to maximize the size of the inverse.

      a.        

 

      b.        

      c.        

      d.        

14.              Find 5 pieces of data of your choice and use your calculator to find a linear regression for that data.

15.              For the following functions determine the following pieces of information:

i.    Determine the end behavior

ii.    Find all possible rational roots.

iii. Use DesCartes’ Rule of Signs to determine the possible number of positive and negative real roots.

iv. Determine if 3 or -3 are upper or lower bounds for the function.

v.                   Determine the possible number of turning points.

vi.                 Find the x-intercepts

vii.                Sketch the graph.

 

  1. f(x) =
  2. g(x) =

16.              For the following rational functions determine the intercepts, asymptotes, holes and sketch the graph.

a.  

b.  

c.  

 

The exam will be of 3 parts:

1.                  A non-calculator portion, about 15 minutes,

2.                  A calculator portion

3.                  A take home portion