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Asymptote
Vertex
Applications
Polynomial
Inequality
100
Find the domain of the following rational function.

-4x2/(x-9)(x+4)

9,-4
100
Use the vertex and intercepts to sketch the graph of the quadratic function. Determine the domain.

f(x)=(x+4)2-9

(-∞,∞)
100
A rain gutter is made from the sheets of aluminum that are 14 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross-sectional area and allow the greatest amount of water to flow. What is the maximum cross-sectional area?
3.5
24.5
100
Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function

-4x7-7x5+5x2+6

The graph rises left and falls right.
100
Solve the polynomial inequality and write the solution set. express the solution set in interval notation.

x2-6x>0

(-∞,0)∪(6,∞)
200
Find the horizontal asymptote, if any, of the graph of the rational function

17x/9x2+2

y=0
200
Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis of symmetry.

f(x)=(x+4)2-9

x=-4
200
The manufacturer of a CD player has found that the revenue R (in dollars) is R(p)=-4p2+1,000p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?
62,500
200
Use the following steps to graph the polynomial function f(x)

-x2(x-3)(x+5)

Use the leading coefficient test to determine the graph's end behavior. What does the graph look like?

Find the x-intercepts. State whether the graph cross the x-axis, or touches the x-axis and turns around, at each point.

What are the x-intercepts?

What does the graph do at x=0?

What does the graph do at the rightmost zero?

What does the graph do at the leftmost zero?

Find the y-intercept

Determine whether the graph has y-axis symmetry, origin symmetry, or neither.

If necessary, find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly.

The graph falls to the left and to the right
0,3,-5
The graph touches the x-axis and turns around.
The graph crosses the x-axis
The graph crosses the x-axis
0
Neither
B
200
Solve the rational inequality and graph the solution set in interval notation.

x-4/x+5

(-∞,-5)∪(4,∞)
300
Find the horizontal asymptote, if any, of the graph of the rational function.

21x2/7x2+6

y=3
300
Use the vertex and intercepts to sketch the graph of the quadratic function. Determine the range.

f(x)=(x+4)2-9

[-9,∞)
300
Farmer Ed has 850 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, find the length and width of the plot that will maximize the area.
Width is 212.5
Length is 425
300
find the zeros for the given polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero.

x3-142+49x

the set of zeros is?

At the leftmost zero?

at the rightmost zero?

0,7
1
2
The graph crosses the x-axis
The graph touches the x-axis and turns around.
300
Solve the polynomial inequality and write the solution set. Express the solution set in interval notation.

5x2+3x<2

(-1,2/5)
400
Find the vertical asymptote, if any, of the graph of the following rational function.

x/x2+6

There are no vertical asymptotes.
400
Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis of symmetry.

f(x)=4x-x2-5

x=2
400
You throw a ball straight up from the rooftop 20 feet high with an initial speed of 112 feet per second. The function s(t)=-16t2+112t+20 Models the balls' height above the ground, s(t), in feet, t seconds after it was thrown, During which time period will the ball's height exceed that of the rooftop?
Between 0 and 7 seconds, excluding t=0 and t=7.
500
Use the vertex and intercepts to sketch the graph of the quadratic function. Determine the range of the function.

f(x)=4x-x2-5

(-∞,-1)