Unit 1A
What is the degree and leading coefficient of this polynomial?
14x^2+6x-2x^6+1
The degree is 6 and the leading coefficient is -2.
Which of the following is true for input values of large magnitude? (a) The polynomial in the numerator dominates the polynomial in the denominator indicating no horizontal asymptote. (b) The polynomial in the numerator dominates the polynomial in the denominator indicating a horizontal asymptote of y=0. (c) The polynomial of the denominator dominates the polynomial in the numerator indicating no horizontal asymptote. (d) The polynomial of the denominator dominates the polynomial in the numerator indicating a horizontal asymptote of y=0. (e) Neither polynomial of the rational function dominates the other indicating a horizontal asymptote of y=1/2
The answer is D.
If each successive term in a sequence has a common difference (or a constant rate of change), the sequence is called what?
It is called an arithmetic sequence.
What test checks to see if a graph is a function?
The Vertical Line Test
As input values increase, if the output values demonstrate a repeating pattern over successive equal-length intervals, it is called a what type of relationship?
It is called a periodic relationship.
Describe the end behavior of this polynomial function using limit notation.
p(x)=-x^3-x^2+x
lim p(x)=∞, x→-∞
lim p(x)=-∞, x→∞
Given f(x)=x^2-3x+2 Let g(x)=2f(x)+4, find g(x)
g(x)=2x^2-6x+8
Write the function along with the input value that represents the output value.
4⋅4⋅4⋅1.5
f(x)=
where x=
f(x)=1.5(4)^x
x=3
Find the value of this log.
logbase2 1/32
logbase2 1/32=y
2^y=1/32 2^y=32^-1 2^y=2^-5
logbase2 1/32
y=5
Describe the concavity of f on the interval, and if f is increasing or decreasing on the interval.
π/2≤θ≤π
cosθ is concave up and decreases at first, but then increases
Find the degree of the polynomial from the given input and output values.
Input: 0,1,2,3,4,5,6,7
Output: 50,49,38,5,-62,-175,-346,-587
This polynomial has a degree of 3.
What is the domain and the vertical asymptote of this rational function?
f(x)=x(x+2)/x^2-4
The domain is (-∞,-2)U(-2,2)U(2,∞).
The vertical asymptote is x=2.
Let f(x)=x^2-4 and g(x)=3-x
a) Find f(g(5))
b) Find g(f(5))
Show your work.
a) g(5)=3-5=-2 f(-2)=(-2)^2-4=0 f(g(5))=0
b) f(5)=(5)^2-4=21 g(21)=3-21=-18 g(f(5))=-18
Find the inverse of a(x)=1/4⋅logbase8 x
4x=4(1/4⋅logbase8 y)
8^4x=8^logbase8 y
8^4x=y=a^-1(x)
In the xy plane, the terminal ray of angle θ in standard position intersects a circle of radius r at the given point. What are the values of θ and r?
(-2, 2√3)
(4⋅-1/2, 4⋅√3/2)
cos 2π/3=-1/2
sin 2π/3=√3/2
r=4
θ=2π/3
What is the average rate of change on the interval
from 13 to 25 seconds? Which formula do you use?
x: 10,13,19,25
y: 80,76,43,30
Formula: y2-y1/x2-x1
Rate of change: -3.833m/s
Answer letters a-f of this. h(x)=2(x+3)(x-3)/(x+2)(x+3) a) Domain: b) Zero(s): c) Hole(s): d) VA: e) HA: f) y-intercept:
a) (-∞,-3)U(-3,-2)U(-2,∞) b) x=3 c) x=-3 d) x=-2 e) y=2 f) -3
Below is a table of values for exponential functions in the form f(x)=a(b)^x+k. Write the equation that represents each table. x: 0,1,2,3,4 f(x): 2,10,34,106,322
1st difference:8,24,72,216 2nd difference:3,3,3
2-a=k 10-3a=k 2-a=10-3a a=4 The equation: f(x)=4(3)^x-2
Find all relevant information from the given function.
f(x)=ln(x-3)+5 Asymptote: Domain: Range: End Behavior:
Asymptote: x=3
Domain: (3,∞)
Range: (-∞, ∞)
End Behavior: f(x)→∞, x→∞ f(x)→-∞, x→3^+
Answer the following of this sinusoid function.
f(θ)=2cosθ Amp: X-int: Max value: Min value:
Amp:2
X-int:π/2, 3π/2
Max value:2
Min value:-2
What is the average rate of change for this function
on the given intervals? Show your work.
y=x^2+4x-2 on -3≤x≤2
The average rate of change is 3.
The data shows the salary in thousands of dollars for employees given their years experience. x Experience(years):2,4,5,8,9,12,15. y Salary(thousands):48,54,58,68,73,80,88 a) Is the Data Linear, Quadratic, or Cubic? b) Write the equation of the regression curve. c) Use your equation to predict the salary of an employee with 11 years of experience.
a) Linear
b) f(x)=3.137x+42.349
c) f(11)=76.856 thousand dollar salary
x(input):100,75,120,200,50,300 y(output):35,22,37,60,20,126
a)Find a linear regression curve b)Use the model from part a to find the error at t=50 c) Is the value predicted an overestimate or underestimate of the actual value?
a) m(t)=0.417t-8.701
b)m(5)=12.149 12.149-20=-7.851
c) The predicted value of 12.149 is an underestimate of the actually value of 20.
Solve the equation.
logbase2 (3x-52)-4= logbase2 (x)
logbase2(3x-52)-logbase2 (x)=4 logbase2(3x-52/x)=4 2^4=3x-52/x 16=3x-52/x 16x=3x-52 13x=-52 x=-4 NO SOLUTION
This is a sinusoid function. Answer the following. y=2sin(x/2)+1 Amp: Period: Midline: Frequency: Max value: Min value:
Amp:2 Period:4π Midline:y=1 Frequency:1/4π Max value:3 Min value:-1