Chapter 1 (Functions)
State the transformations:
y=f(3x)+1
Horizontal compression by 1/3 and up 1
What is the equation of the vertical asymptote?
f(x)=(x^2-9)/(x^2-2x-15)
x=-3
Evaluate:
log_2(1/16)
-4
A 12 foot ladder is leaning against a wall. The bottom of the ladder is 18 inches from the wall. What is the angle of elevation formed by the ladder and the ground?
82.819^o
Complete the quotient identity:
sintheta/costheta= ?
tantheta
What is the name of that baby that fell down the well in 1987?
Jessica
Find f(x+h):
f(x)=5x^2-3x
5x^2+10xh+5h^2-3x-3h
Find the remainder:
(x^4-5x^2+17x+11)/(x+3)
-4
Write in exponential form:
lnx=5
x=e^5
Find the exact value:
tan((11pi)/6)
-sqrt3/3
Simplify. (Write as a single trigonometric function)
sintheta/(1-cos^2theta
csctheta
What was the GNC before it was the GNC?
Sandburg
State the domain using interval notation:
f(x)=sqrt(x+1)/(x-3)
[-1, 3)uu(3,oo)
Divide:
(2x^4-9x^3-43x^2+36x+145)/(2x^2-9x-35)
x^2-4+5/(2x^2-9x-35)
Solve. Round to three decimal places.
5(3)^(x-1)=20
x=2.626
What is the maximum value of this function?
f(x)=-5cos(2x-pi)+11
16
Simplify as far as possible:
cos((3pi)/8)cos(pi/8)+sin((3pi)/8)sin(pi/8)
sqrt2/2
Find the sum:
sum_(k=0)^5(k^3)
225
Find the AROC from x = -1 to x = 3 for
f(x)=x^2
2
Find all of the zeros by factoring:
f(x)=2x^3-3x^2+14x-21
x=3/2, x=isqrt7, x=-isqrt7
Solve. Round to three decimal places.
2e^(x+3)+4=34
x=-0.292
sintheta=-2/5, costheta>0, cottheta=?
cottheta=(-2sqrt21)/21
Find all solutions in the given interval:
2 cos^2x+cosx-1=0; [0,2pi]
theta=pi/3, (5pi)/3, pi
Find the limit:
lim_(x->5)((x^2+2x-35)/(x-5))
12
f(x)=e^(x+1), g(x)=ln(x)-1
Find f(g(x)).
x
What is the most amount of zeros this function can have?
f(x)=4x^3-3x^5+7x-1
5
Expand:
log(x^4/sqrt(x-5))
4logx-1/2log(x-5)
arcsin(-sqrt2/2)
-pi/4
tantheta=-5/12, pi/2<theta<pi, cos2theta=?
cos2theta=119/169
What bizarre gift did one of my students give me many years ago?
a bag of skin