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Math 1113 Pre-Calculus Quiz 1 Practice Summer 2008
Name: Last ___________________, First ______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
- 6(x - 1)
(x + 1)
A) Yes; degree 72 B) Yes; degree 12 C) Yes; degree 6 D) Yes; degree 15
- f(x) =
x
x
A) Yes; degree 3 B) Yes; degree - 3
C) Yes; degree 5 D) No; it is a ratio of polynomials
For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x
axis at
each x - intercept.
- f(x) = x +
(x - 2)
A)
, multiplicity 4, touches x
axis;
2, multiplicity 5, crosses x
axis
B)
, multiplicity 4, crosses x-axis; - 2, multiplicity 5, touches x-axis
C)
, multiplicity 4, touches x
axis; 2, multiplicity 5, crosses x
axis
D) -
, multiplicity 4, crosses x-axis; 2, multiplicity 5, touches x-axis
Form a polynomial whose zeros and degree are given.
- Zeros: 2 , multiplicity 2; - 2 , multiplicity 2; degree 4
A) f(x) = x
C) f(x) = x
- Zeros: 0, - 7 , 6 ; degree 3
A) f(x) = x
- 42x for a = 1 B) f(x) = x
C) f(x) = x
- 42x for a = 1 D) f(x) = x
Use the x
intercepts to find the intervals on which the graph of f is above and below the x
axis.
- f(x) =
(x
A) above the x
axis: no intervals
below the x-axis: (-∞, 4), (4, ∞)
B) above the x
axis: ( 4 , ∞
below the x-axis: (-∞, 4)
C) above the x-axis: (-∞, 4 ), ( 4 , ∞)
below the x-axis: no intervals
D) above the x-axis: (-∞, 4 )
below the x-axis: (4, ∞)
Find the x- and y-intercepts of f.
- f(x) = (x + 6 )(x - 3 )(x + 3 )
A) x-intercepts: - 6 , - 3 , 3 ; y-intercept: 54 B) x-intercepts: - 6 , - 3 , 3 ; y-intercept: - 54
C) x-intercepts: - 3 , 3 , 6 ; y-intercept: - 54 D) x-intercepts: - 3 , 3 , 6 ; y-intercept: 54
Form a polynomial whose zeros and degree are given.
- Zeros: - 5 , multiplicity 2; 2 , multiplicity 1; degree 3
A) x
C) x
Find the vertical asymptotes of the rational function.
- R(x) =
x
A) x = 11 , x = - 4 B) x = - 44
C) x = - 11 , x = 4 D) x = - 11 , x = 4 , x = - 3
- F(x) =
x
x
5x
A) x = -
1 B) x = -
1, x = -
4 C) x
1, x = -
4 D) x = -
1, x
Give the equation of the oblique asymptote, if any, of the function.
- f(x) =
2x
x
A) y = 2x - 1 B) y = 0 C) y = 2x + 1 D) y = 2x
Graph the function.
- f(x) =
x
x
x
-10 -5 5 10
y
10
5
x
-10 -5 5 10
y
10
5
Solve the problem.
- Economists use what is called a Leffer curve to predict the government revenue for tax rates from
0% to 100%. Economists agree that the end points of the curve generate 0 revenue, but disagree on
the tax rate that produces the maximum revenue. Suppose an economist produces this rational
function
R(x) =
10x(100 - x)
x
, where R is revenue in millions at a tax rate of x percent. Use a graphing
calculator to graph the function. What tax rate produces the maximum revenue? What is the
maximum revenue?
A) 28.1%; $470 million B) 31.4%; $464 million
C) 29.7%; $467 million D) 26.5%; $469 million
Solve the inequality. Express the solution using interval notation.
- x(x
x) ≥
A) [
3, 5] B) [
3, 0] or [5, ∞
) C) (
3] or [0, 5] D) [0, 5]
- x
A) (-∞, - 3 ] or [ 3 , ∞) B) (-∞, 3 ]
C) [- 3 , 3 ] D) [ 3 , ∞)
x - 2
x
A) (
4 , 2 ) B) (
C) (
4 ) or ( 2 , ∞
) D) (
Use the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real
numbers.
- f(x) = x
A) - 4 , - 5 , 4 , 5 ; f(x) = (x - 4 )(x + 4 )(x - 5 )(x + 5 )
B) - 5, 5; f(x) = (x - 5)(x + 5)(x
C) 4; f(x) = (x - 4)
(x
D) - 4, 4; f(x) = (x - 4)(x + 4)(x
- f(x) =
3x
14x
7x
A) - 1,
, 5; f(x) = (3x - 2)(x - 5)(x + 1) B) 1,
, - 5; f(x) = (3x - 2)(x - 1)(x + 5)
C) - 1,
, - 5; f(x) = (3x - 2)(x - 5)(x + 1) D) - 5,
, 1; f(x) = (3x - 2)(x - 1)(x + 5)
Find the intercepts of the function f(x).
- f(x) = 2x
(x - 5)
A) x-intercepts: 0, - 5 ; y-intercept: 0 B) x-intercepts: 0, - 5 ; y-intercept: 2
C) x-intercepts: 0, 5 ; y-intercept: 2 D) x-intercepts: 0, 5 ; y-intercept: 0
Solve the equation in the real number system.
- x
A) {- 4 , - 2, 2, 4 } B) {- 4 , 4 } C) {- 8 , 8 } D) {-2, 2}
Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
- Degree 5; zeros: 3 , 6 + 5i, - 3 i
A) - 6 + 5i, 3 i B) 6 - 5i, 3 i C) - 6 - 5i, 3 i D) - 3 , 6 - 5i, 3 i
- Degree 6; zeros: 3 , 3
i,
i, 0
A)
i,
i B)
i, 1
i C) 3
i,
i D)
i, 1
i
Form a polynomial f(x) with real coefficients having the given degree and zeros.
- Degree: 3; zeros: - 2 and 3 + i.
A) f(x) = x
C) f(x) = x
Use the given zero to find the remaining zeros of the function.
- f(x) =
x
10x
42x
124 x
297x
306 ; zero: 3i
A)
3i, 4
i, 4
i B) 2,
3i,
i,
i
C) 2,
3i, 4
i, 4
i D)
3i,
i,
i
Find all zeros of the function and write the polynomial as a product of linear factors.
- f(x) = x
A) f(x) = (x - 1)(x - 12 )(x - 2 i)(x + 2 i) B) f(x) = (x - i 12 )(x + i 12 )(x - 2)(x +2)
C) f(x) = (x + 4 )(x + 3 )(x - 2 i)(x + 2 i) D) f(x) = (x - 4 )(x + 3 )(x - 2 )(x + 2 )
