MATH 241
Quiz 1
Name __________________
Instructor: Brian Balman
1. Find the domain and range of
2. Which equations determine y as a function of x?
(a)
6x! 5y2 + 4 = 0
(b)
y = x2 + 6
3. Determine whether
is even, odd, or neither even nor odd.
4. Determine the interval(s) on which the function is increasing:
5.
Given
6.
Given
and
, find f B g (x)
, find
7. A circle has this equation: ( x ! 5) 2 + ( y + 3) 2 = 49
What is the center?
What is the radius?
8. Test
x = y (2 ! x 2 )
for symmetry with respect to the origin.
9. Find the number of units x that produce a minimum cost C if C = 15000 ! 600x + 0.03x2.
10 Determine the right- and left-hand behavior of the graph of the polynomial: f(x) = 2x4 ! 5x3 + 17
11 Write a polynomial equation in factored form for the graph:
12. What three statements are equivalent to “ (x ! 2) is a factor of
.” ?
13. Divide:
=
14. Use synthetic division to find f(-5):
f(x) = 4x3 + 7x2 ! 5x + 10
15. List all possible rational zeros:
16. Find all zeros of
f(-5) =
g(x) = 3x3 ! 2x2 + 15x ! 12
f(x) = x5 + x3 + 2x2 ! 12x + 8.
17. Find the asymptotes:
18. Find the slant asymptote:
19. The concentration of a certain medication in the bloodstream t hours after injection into muscle
tissue is
Determine the horizontal asymptote of the function.
20. Find an equation for the following graph. Use your grapher to check your answer.
21. Solve for x:
53x = 40
22. Solve for x: log(x + 4) + log(x + 1) = 1
23. Find all zeros of
f(x) = x4 ! 3x3 + 6x2 + 2x ! 60.
True or false:
_________ 24.
The degree of a polynomial is the number of zeros it has.
_________ 25.
The maximum number of turns that the graph of a polynomial can
make is always the same as its degree.
_________ 26.
The number of y-intercepts that a graph of a polynomial has is
always one.
_________ 27.
The Quadratic Formula is used to find irrational and complex
zeros a polynomial.
_________ 28.
Quadratic functions always have two real zeros.