Unit 1
What is the degree of
f(x)=5x^6-7x^8+4x^7
8
In polynomial g(x), what is the root behavior at x=3?
g(x)=x(x-2)^3(x-3)^2
Bounce
State the domain of
(x^2+x-6)/(x^2-2x)
x cannot be 0 or 2
Identify the vertical asymptotes of
(x^3-3x^2-4x)/(4x^2+8x-12)
x=-3 and x=-1
log_4(64)=?
3
Simplify
(2x-7)^2
4x^2-28x+49
Write the end behavior of the function in limit notation.
h(x)=-x^3+2x^2-5x+10
lim_(x->-oo)h(x)=oo
lim_(x->oo)h(x)=-oo
Factor x3-27
(x-3)(x2+3x+9)
lim_(x->3)(x+2)/(x^2+2x+1)=?
5/16
Find the domain of the function.
f(x)=log_4(-x+5)
x<5
What is the remainder of
(3x^3+x^2-5x-7)/(x-2)
11
Is (x-2) a factor of
f(x)=x^3-x^2-x-2
Yes
Simplify the expression and state the domain.
(x-7)/(x^2-4)/(x^2-6x-7)/(2x+4)
x cannot be 2, -2, 7, or -1
2/((x-2)(x+1)
Find the holes (x and y coordinates), vertical asymptotes, and end behavior asymptote.
g(x)=(2x^3+8x^2)/(x^3+2x^2-8x)
Holes: (0,0), (-4,4/3)
Vertical asymptote: x=2
End behavior asymptote: y=2
Expand the logarithm.
log_3(uv^3)^3
3log_3u+9log_3v
(x^3-7x^2-5)/(x^2-4x+6)
x-3-(18x-13)/(x^2-4x+6)
Find all roots of
f(x)=2x^4-9x^3+13x^2-81x-45
x=5, -1/2, 3i, -3i
Simplify the expression
x/(x^2+5x+4)+5/(x+1)
(6x+20)/((x+1)(x+4)
Solve.
-10/(x+5)<=-11/(x+6)
(-oo,-6)U(-5,5]
Solve. Give exact answers.
3^(2x)+2*3^x-24=0
x=log_3(4)
Find the x7 term in the expansion of
(2x-5)^9
115,200x7
Build a polynomial of least degree that has roots x=3(mult 2) and 4i
f(x)=x^4-6x^3+25x^2-96x+145
Solve the equation.
5/(y-1)+3/(y-3)=8/(y-2)
y=6
A boat can travel 16 miles up a river in 2 hours. The same boat can travel 36 miles downstream in 3 hours. If the speed of the current is 2 mph, what is the speed of the boat in still water?
10 mph
Solve.
ln(x+5)=ln(x-1)-ln(x+1)
No solution