Semper Fi
Simplify.
5/(6+\sqrt{3})
\frac{30-5\sqrt{3}}{33}
Solve
2x^2-11x+5=0
x=1/2, 5
How can you tell whether a graphed relation is a function or not?
A graphed relation is a function if everywhere you draw a vertical line, you only intersect the relation in exactly one place. (the vertical line test)
Determine the domain and range of the function. Write your answer in interval notation.
f(x)=2x^2-2x-12
Domain: (-inf, inf)
Range: [-12.5, inf)
Evaluate the expression.
log(log_5 5^10)
1
Solve the system.
x-2y=-8
4x+5y=20
(0, 4)
Factor.
x^3+5x^2-x-5
(x-1)(x+1)(x+5)
Solve.
\sqrt{8-2x}-x=0
x=2
Determine the average rate of change of the function in the interval [-2,8].
f(x)=-9x^2-2x
\frac{f(8)-f(-2)}{8-(-2)}=\frac{-592+32}{10}=-56
Determine the leading term, degree, and end behavior of the polynomial.
g(x)=x^4-6x^3+8x^2+6x-9
LT: 1, Degree: 4, EB: Both Up
Solve.
3^{2x-1}=7^{x+1}
x=\frac{ln7+ln3}{2ln3-ln7}
Solve the system.
3x+2y=38
y-2x=12
(2,16)
Simplify.
\frac{2x}{x^2-9}-\frac{4}{x+3}
\frac{-2x+12}{x^2-9}
Solve.
2|x-3|-6=10
x=-5, 11
Determine whether the function is even, odd or neither.
\varepsilon(x)=1/5x^6-3x^2+1
Neither. Plug in -x in for x in the function and you do not get back either the same function nor the negative version of the function.
Determine the zeros, their multiplicity and whether the graph is tangent or crosses at those zeros.
\pi(x)=x^3-x^2-16x+16
Zeros: -4, 1, 4
Mult: 1, 1, 1
Tan/Cross: Cross, Cross, Cross
Solve.
logx+log(x+3)=1
x=2
Solve the system.
x^2+y^2=1
y-x=0
(\sqrt{2}/2,\sqrt{2}/2), (-\sqrt{2}/2,-\sqrt{2}/2)
Simplify.
2\sqrt{50}+3\sqrt{8}
16\sqrt{2}
Solve. Write your answer in interval notation.
|2x+5|-7\geq -6
(-\infty, -3)\cup(-2,\infty)
Given the two functions determine (n o m)(x).
m(x)=\sqrt{1-x}, n(x)=2x^2+4
(n\circm)(x)=-2x+6
Give a third power polynomial with zeros -3i and 2, such that f(-2) = -208.
g(x)=4x^3-8x^2+36x-72
Describe the changes to the horizontal asymptote and y-intercept of the parent function for the function.
h(x)=-e^x+5
The graph will shift up five units and reflect over the y-axis.
The HA will become y=5 and the y-intercept will become (0, 6).
Determine the quadratic function whose graph passes through the points (-1,-2), (2,1), and (-2,1).
y=x^2-3
Simplify.
(-5x^3y^2)(-2x^{-11}y^{-2})
10/x^8
Find the inverse of the function.
\rho(x)=x/(x+1)
\rho^{-1}(x)=x/(1-x)
Determine the difference quotient for the function.
\frac{f(x+h)-f(x)}{h}, f(x)=-3x^2-2x+1
-6x-3h-2
Determine all the zeros of the polynomial.
\omega(x)=x^3+4x^2+9x+6
x=-1, \frac{-3\pmi\sqrt{15}}{2}
Solve the equation.
e^{4x}-5e^{2x}-24=0
x=ln8/2
A rectangular plot of land is fenced along three sides using 39 feet of fencing. The remaining side will not have fence. If the area of the plot is 180 square feet, what are the dimensions of the plot of land?
12 by 15 or 7.5 by 24