Better than 1 bola
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
Ms. Carmack's last day
Tuesday 11/26
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
Describe the symmetry of the following function:
f(x) = 4x-2
About the y-axis
Consider the function f(x)=4x3-x2-2x+27.
What is the quotient if f(x) is divided by (x+2)?
4x2-9x+16
Ms. Carmack's favorite band
The Beach Boys
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
Using the leading term, state the end behavior of the polynomial:
f(x) = -5x6 + 4x5 - 15x4 + 3x3 - 2x + 1
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
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)
Use the factor theorem to determine which binomials are factors of the given function:
f(x) = 4x4 + 52x3 +87x2 - 13x - 22
(x-1), (x+11), (x+2)
(x+11) and (x+2) are factors
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
State the domain, range, x-intercept(s), y-intercept(s), increasing interval, decreasing interval, symmetry, discontinuities, and end behavior of the following function:
f(x) = -2x5
domain: all real #s, range: all real #s
x int: (0,0), y-int: (0,0), increasing interval: none,
decreasing interval: (-infinity, 0)U(0,infinity)
symmetry: about the origin
discontinuities: none
As x approaches infinity, f(x) approaches -infinity
As x approaches - infinity, f(x) approaches infinity
The relative maximum(s) and minimum(s) of this function:
f (x) = x5 - 4x3 + 2x + 3
relative minimums:
(-0.4, 2.4), (1.5, 0.1)
relative maximums:
(-1.5, 5.9), (0.42, 3.6)
Use the factor theorem and the given binomial to completely factor the polynomial function. Then, give the zeros:
f(x) = 9x4 - 18x3 - 73x2 + 2x + 8; (x+2)
f(x) = 9x4 - 18x3 - 73x2 + 2x + 8
f(x) = (x+2) (3x+1) (3x-1) (x-4)
x = { -2, -1/3, 1/3, 4}
DOUBLE JEOPARDY: Find the removable discontinuity of the following function:
f(x)=(x2-49)/(x2+4x-21)
x=-7