Math 1111
Test #2, Chapter 3
Name ______________________________
SHOW ALL WORK FOR FULL CREDIT.
2
I. Consider the quadratic function f ( x)  3 x  12 x  4 .
a.
Give the coordinates of the vertex of the graph of f. ________________________
b.
Give the equation of the axis of symmetry. _________________________
c.
Give the coordinates of each x-intercept. __________________________
d.
Give the coordinates of the y-intercept. __________________________
e.
Sketch the graph of f and label a-d on the graph.
f(x)
X
II.1. Consider the rational function
g ( x) 
3x
2
2
x 9
.
a.
Determine the domain. ______________________________
b.
Give the coordinates of each x-intercept. __________________________________
c.
Give the coordinates of the y-intercept. _____________________
d.
Determine whether g is even, odd, or neither. ____________________
e.
Write the equation of each vertical asymptote. __________________________
f.
g.
Write the equation of each horizontal or oblique asymptote and give the coordinate pairs of
each, if any, point where the graph intersects it. ____________________________________
Determine the intervals where the graph is above and where it is below the x-axis.
___________________________________________________________
h.
Sketch the graph of g.
g(x)
X
2
2 x  8 x  10
2. Consider the rational function: h( x) 
.
x3
a.
Find and list the horizontal/oblique asymptotes _______________________________
b.
Find and list the vertical asymptotes ______________________________
c.
Find and list the x and y-intercepts ____________________________
III. Consider the polynomial function f ( x)  3 x x  3  x  1 .
2
a.
Find the x and y intercepts of f ____________________________
b.
Determine whether the graph of f crosses or touches the x-axis at each intercept
_________________________________________________________
IV.
c.
Find the power function that the graph of f resembles for large values of x ____________
d.
Determine the maximum number of turning points on the graph of f __________
e.
Graph f using intervals (x-intercepts as endpoints of the intervals)
A. Find all the zeros (real and complex) of the given polynomial. Use the zeros to factor f over the
real numbers.
3
2
f ( x)  x  3x  6 x  8
B. Find a polynomial of degree three with zeros of -3 and 1+ i.
V. Write each expression in standard form
a.
 6  3i    2  2i 
a  bi .
b. 1  i 
2
VI. Solve the equation in the complex number system.
4
2
x  8x  9  0
Bonus: What is the maximum number of squares in this figure?
c.
i
13