Work each of the fol lowing problems and make sure to
show all your work. Each problem will have a value of 10 points .
1. Sketch the graph of the quadratic function
defined by
Provide the
following information.
Vertex : ( , )
y- intercept : ( , )
axis:
Range:
Use synthetic division to find the quotient q(x) and the remainder r.
3. Use synthetic division to find f (2) , if
4. x-3 is a factor of
What is the other factor?
5. The cost of producing x units of a certain commodity is
given by
A) How many units are necessary to minimize the cost? B) What is the minimum
cost?
For problems 6 - 8, consider the polynomial
6. Use the Rational Zeros Theorem to list all possible
rational zeros.
7. Use Descartes' rule of signs to de termine the number of
possible positive real zeros.
8. If 2 is a zero of the polynomial, find the other zeros.
9. Graph the rational function and provide the requested
information:
Equation(s) of vertical asymptote(s):
Equation(s) of horizontal asymptote(s):
y-intercept(s):
x-intercept(s):
10. Give the equation of the oblique asymptote for the
rational function
11. Sketch the end behavior of the graph of each of the
following.
12. A polynomial of degree 4 with real coefficients has 4
zeros . If three of the zeros are 8 + i ,-6, 2 find the fourth zero.
13. If 1 is a zero of
,
factor f(x) into linear factors .
f(x)=
14. If a polynomial with real coefficients has 7 turning
points, what is the smallest degree that the polynomial can have?
Answers
1.
Vertex: (2 , 1)
y-intercept: ( 0 , 5 )
axis: x = 2
Range: [1,∞)
The
other factor is x2+x+2.
5.
A) 25 units
B) $469,640
6. ±1.±2.±4.±7.±14.±28
7. 2 or 0 (Because there are two variations in sign )
8. -2,7
9. Equation(s) of vertical asymptote(s): x=4, x=−4
Equation(s) of horizontal asymptote(s): y=0
y-intercept(s): (0 , 0)
x-intercept(s): (0 , 0)
10.
The
equation of the oblique asymtpote is4.y=x−4
11. A) ↓↑ B) ↓↓ C) ↑↓
12. 8 − i
13. f(x)=(x−1)(x+1)(x+3)
14. 8
Note: Graphs are not shown.
