Quadratic Functions and Inequalities
Use interval notation to express the following:
The set of all number greater than or equal to -15 and less than -2
[-15,-2)
Is the following a power function, a polynomial, both or neither?
f(x)=-17x5
Both Power and Polynomial
Find the x-intercepts and y-intercept of the following function:
f(x)=(x-1)(x+1)(x+2)
Answer as a list of ordered pairs (x,y) separated by commas
x-int: (-2,0), (-1,0), (1,0)
y-int: (0,-2)
Consider the function f(x)=x3+4x2-25x-50.
If there is a remainder of 50 when the function is divided by (x-a), what is the value of a?
5, -5, 3, -3
-5
Which are the intercepts (x and y) of the following function:
f(x)=((x-6)(x+1))/((x-1)(x+3)(x+6))
x-int: x=6,-1
y-int: y=1/3 or 0.333
Determine the domain and range of the following parabola:
f(x)=-(x+5)2-4
Domain is all real numbers. Range is f(x) less than or equal to -4.
Which of the following are power functions?
A) f(x)=5*3x
B) f(x)=5*14x
C) f(x)= cube root of x
D) f(x)=2*14x
E) f(x)=5/x9
C and E
What are the two types of multiplicities and what are their behaviors in a graph?
Even bounces and odd crosses
Consider the function f(x)=x3+3x2-51x+91.
What is the remainder if f(x) is divided by (x+9)?
64
What are the vertical asymptotes of the following function?:
f(x)=(x2-3x-4)/(x2-9x+8)
x=1 and 8
Find the x-intercept(s) of the following function:
f(x)=10x2+23x-42
(Whole number or fraction: NO DECIMALS)
(-7/2,0) and (6/5,0)
Which of the following are polynomial functions?
A) f(x)=4*11x
B) f(x)=3*18x
C) f(x)=10*17x
D) f(x)=-4x3-4x2+5x+1
E) f(x)=-2x-1
D and E
Given that a polynomial has a degree 4, what is the number of turning points?
At most 3
Consider the function f(x)=4x3-x2-2x+27.
What is the quotient if f(x) is divided by (x+2)?
4x2-9x+16
What is the horizontal asymptote of the following function?:
f(x)=(x3-x+12)/(x5+3x2-2)
y=0
An object is launched directly in the air at a speed of 144 feet per second from a platform located 12 feet in the air. The motion of the object can be modeled using the function f(t)=-16t2+144t+12, where t is the time in seconds and f(t) is the height of the object. When, in seconds, will the object reach its maximum height? After how many seconds will it touch the ground? Round to the nearest tenth
Maximum height: 4.5
Ground: 9.1 seconds
Describe the end behavior of the following function:
f(x)=-0.4(2x-9)(3x+1)(x-7)(x+9)(3x-1)
rising as x approaches negative infinity and falling as x approaches positive infinity
Given that a polynomial has 9 turning points, what is its degree?
At least 10
Use synthetic division to find the result when 2x4-12x2+5x-46 is divided by x+4. Write your answer in the form q(x)+(r(x)/d(x)).
2x3-8x2+20x-75+(254/x+4)
What is the horizontal asymptote of the following function?:
f(x)=(12x4-3x2+5)/(3x4-1)
y=4
Describe the graph of the parabola f(x)=-2x2+10x+24.
Make sure to include the direction in which it opens, the vertex, the axis of symmetry, the x intercepts, and the domain and range.
Round your answers to the nearest tenth.
Direction in which it opens: down
Vertex: (2.5, 36.5)
Axis of symmetry: x=2.5
x-int: x=-1.8 and 6.8
Domain: All real numbers
Range: f(x) is less than or equal to 36.5
What 2 things do you have to look for to identify the graph of a polynomial function?
Hint: The graph of a polynomial function is a smooth, connected line.
-No Corners
-No Asymptotes
Write an equation with a degree of 3, x-intercepts located at (7,0) and (-3,0), and a y-intercept located at (0,84).
f(x)=(x+3)(x-4)(x-7)
What is the slant asymptote of the graph f(x)=(12x2-9)/(3x)?
4x
Find the removable discontinuity of the following function:
f(x)=(x2-49)/(x2+4x-21)
x=-7