Introduction to Polynomial Functions
State the degree and the leading coefficient of the polynomial
y= 5x4 - 3x3 + 4
Degree = 4
Leading coefficient = 5
Even, odd, or neither
f(x) = x2 - 2x
Neither
Rewrite the equation in logarithmic form
5-2 = 1/25
log5 (1/25) = -2
Determine the exact radian measure of the angle
200°
10π/9
Determine the average rate of change for the following on the interval -1≦ x ≦ 2
g(x) = 3(2)x
△f(x)/△x = 3.5
Long Division
(m2-7m-11)÷(m-8)
m ÷ 1 - 3 / m - 8
Match the function with the corresponding transformation of y=xn
y=(-x)n+2
a) no reflection
b) reflection in the x-axis
c) reflection in the x-axis and the y-axis
d) reflection in the y-axis
d) Reflection in the y-axis
Evaluate
log 100-4
-8
Determine the exact value of the following
sec (7π/4)
√2
Solve
logx<2x
x>0
Factor each and find all zeros
f(x) = x3 + 9x2 + 23x + 15; x + 5
Factors to: f(x) = (x + 1)(x + 3)(x + 5)
Zeros: {-1,-3,-5}
The profit function for a company selling widgets is given by p(x)= -2x2 + 5x -2 where x is the number of widgets sold. The average profit per widget is given by: A(x) = p(x) / x
Write the defining statement for A(x)
A(x) = -2x2 + 5x -2 / x
Solve for x
100 = 10 log 1000x
x = 3.333
State the period, amplitude, phase shift and the equation of the axis of the curve
g(x)= -cos (x - 2π) -3
Vertical reflection
Horizontal shift right 2π units
Vertical shift down three units
Given the function f(x)=3x3-4x and g(x)=2x2-3 determine an equation for
(fg)(x)
(fg)(x) = 6x5-17x3+12x
Solve the inequality
2 - 2x ≦ x - 8
x ≧ 10 / 3
State the domain, range, vertical and horizontal asymptotes
f(x) = 1 / (x+3)(x-5)
Domain: {x l x ≠ -3, x ≠ 5, xER}
Range: {y l y ≠ 0, yER}
Vertical Asymptotes: x = -3 and x = 5
Horizontal Asymptotes: y = 0
Solve
log3(x+4)+log3(x-4) = 2
x=5
Solve the following on the interval 0 ≦ ø ≦ 2π
5sin ø - √3 = 3sin ø
ø= π/3, ø = 2π/3
In the advertisments of a certain bathroom cleaner, the product promises to eliminate 99% of bacteria. The function f(x) = 100(0.85)x represents the percent of bacteria that are still alive at a time x, in minutes.
Determine the average rate of change over the first 5 minutes
-11.13% bacteria/min
Write a rule for the sign function s(n): s(n) is -1 when n is negative, +1 when n is positive, and 0 otherwise
s(n) = {-1, n<0}
{0, n=0}
{1, n>0}
A vertical asymptote at x=2, a horizontal asymptote at y=0, no x-intercept and a y-intercept at (0,3)
f(x) = -6 / x-2
Solve
48(1.03)x=96
x=23.45
The water at a local beach has an average depth of 1 metre at low tide. The average depth of the water at high tide is 8 meters. One cycle of the tides takes approximately 12 hours.
Determine an equation for the periodic function assuming the water level is at the low tide mark at midnight (t=0)
f(t) = 3.5cos [π/6 (t-6)] + 4.5
Let f(x) = √x-9 and g(x) = 1/x2. Write a simplified algebraic model for each composite function. State the domain and the range of each.
y=f(g(x))
y = √1-9x2 / x, x≠0
Restrictions: -1/3 ≦ x ≦ 1/3, x ≠ 0
Domain: {xER, -1/3 ≦ x < 0, 0< x ≦ 1/3}
Range: {yER}