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Vocabulary
Rational Functions
Polynomials
Word Problems
Asymptotes
100
What is a quadratic function?
A polynomial of degree 2.
100
Solve: x+5 = 14/x
x = 2, x = -7
100
Write an equation for the linear function f, satisfying the given conditions: f(-5)=-1, f(2)=4
f(x)=(5/7)x+8/7
100
Mr. Redman bought an imac and it depreciated over 5 years using the straight line method. If its initial value was $2350, what is its value 3 years later?
$940
100
Find the horizontal and vertical asymptotes of: f(x) = 1/x
horizontal: y = 0 vertical: x= 0
200
What is the axis of a quadratic function?
The line of symmetry.
200
Solve: x + 10/x = 7
x=2, x=5
200
Find the vertex and axis of the graph of: f(x)=3(x-1)^2+5
Vertex: (1,5); axis: x=1
200
Mr. Redman designed a rectangular patio that is 25 ft by 40 ft. This patio is surrounded by a terraced strip of uniform width planted with small trees and shrubs. If the area A of this terraced strip is 504 ft squared, find the width x of the strip.
3.5 feet
200
Find the horizontal and vertical asymptotes of: f(x) = x/(x-1)
Horizontal: y = 1 Vertical: x = 1
300
What is a rational function?
A ratio of polynomial functions.
300
x + 12/x = 7
x = 3, x=4
300
Find the vertex and axis of the graph of: f(x)=3x^2+5x-4
Vertex: (-5/6, -73/12); axis: x= -5/6
300
I-70 has a section posted as a 6% grade. This means that for a horizontal change of 100 ft there is a 6-ft vertical change. Find the slope of the highway.
6/100 or 0.06
300
Find the horizontal and vertical asymptotes of: f(x) = (3x^2 + 1)/(4x^2 + x + 1)
Horizontal: 3/4 Vertical: none
400
What is the vertex of a parabola?
The point on the parabola that intersects its axis.
400
3/(x+2) + 6/(x^2+2x)=(3-x)/x
x=-2, x=0, but both solutions are extraneous, so no real solutions
400
Describe the end behavior of: f(x)=3x^4-5x^2+3
infinity,infinity
400
I-70 has a section posted as a 6% grade. This means that for a horizontal change of 100 ft there is a 6-ft vertical change. On a highway with a 6% grade what is the horizontal distance required to climb 250 ft?
about 250 ft
400
Find the horizontal and vertical asymptotes of: f(x) = x^5/9x^6
Horizontal: y = 1 Vertical: x=0
500
(x^2-2x+1)/(x+5)=0
x=1
500
Describe the end behavior of: f(x)=7x^2-x^3+3x-4
-infinity, infinity
500
A box company wishes to design boxes with a volume not more than 100 in cubed. Squares are to be cut from the corners of a 12-in by 15-in piece of cardboard, with flaps folded up to make an open box. What size squares should be cut from the cardboard?
x should be between 0 and 0.69 or x should be between 4.20 and 6