Polynomials
State the degree and the leading coefficient of the function $f(x) = -2x4 + 5x3 - x + 7.
Degree: 4
Leading coefficient: -2
What are the vertical asymptote and horizontal asymptote of f(x) = (2x + 1)/(x - 3)?
VA at x=3
HA at y=2
Solve for x; 2x=32
x=5
convert 3π/4 radians to degrees
135°
What is the equation to calculate Average Rate of Change of f(x) on the interval a ≤ x ≤ b
[f(b) - f(a)]/(b-a)
How can you tell if a function has even symmetry?
if f(-x)=f(x)
What creates a hole in the graph of a rational function?
An x value that makes both the numerator and denominator equal 0
Simplify into a single logarithm: log(x) + 2log(y) - log(z)
log(xy2/z)
What is the amplitude and period of y = -3sin(2x - π) + 1?
Amplitude: 3
Period: π
If f(x) = x2 and g(x) =2x + 1, what is (f ∘ g)(x) at x = 4
81
If a polynomial function has a zero at x = 3 with a multiplicity of 2, how does the graph behave at the x-axis at x = 3?
It bounces off of x=3
x=-7/2
Solve for x: 32x-1 = 27
x=2
What is the exact value of cos(11π/6)?
√3/2
Find the instantaneous rate of change of f(x) = x2+3x at x=4
11
State the x-intercepts and the y-intercept of the function f(x) = -2(x + 1)(x - 2)2.
x-intercepts at x=-1, x= 2
y-intercept at y=-8
State domain and any critical points of this equation (x2-9)/(x-3)
{XER| x=/ 3}
Y-int at y=3
X-int at x=-3
Hole at x=3
No HA
No VA
Solve for x (remember domain restrictions): log3(x) + log3(x - 2) = 1
x=3
Solve √2sin(x) + 1 = 0 for 0 ≤ x ≤ 2π
x= 5π/4
x= 7π/4
A rocket's height in meters is given by h(t) = -5t2 + 40t. What is the average rate of change of the height from t = 1 to t = 3 seconds?
20 meters
Solve the polynomial inequality x3 - 4 ≥ 0 using an interval/sign chart. (Use the correct notation)
{x|-2 ≤ x ≤ 0, 2 ≤ x, XER}
Solve the inequality (x+2)/(x-2) ≤ 0 (use the correct notation)
{x|-2 ≤ x<1, XER}
A sample of 100g of a radioactive substance decays with a half-life of 5 years. How much remains after 12 years? (Round to one decimal place).
18.9g
Prove the identity: sin(2x)/[1+cos(2x)] = tan(x)
LS = RS
If (f ∘ g)(x) = 4x2-6x+5 at x=x, solve for g(x) and f(x).
g(x) = 2x, f(x) = x2-3x+5
g(x) = -2x, f(x) = -x2+3x+5
g(x) = 4x2-6x, f(x) = x+5
A lot of possible answers