Functions Potpourri
The domain of:
f(x)=\frac{1}{\sqrt{x+2}}
Domain:
(-2,\infty)
Find the values of the remaining 5 trig ratios given
tan(theta)=1/13
sin(theta)=1/\sqrt(170)=sqrt(170)/170
cos(theta)=13/\sqrt(170)=(13sqrt(170))/170
csc(theta)=sqrt(170)
cot(theta)=13
State the end behavior of the function:
P(x)=-3x^4+5x^3-7
x\to-\infty, y\to -\infty
x\to+\infty, y\to -\infty
Evaluate log_2(8)
3
Find the exact value
cos^(-1)(cos(-\pi/7))
(6pi)/7
The range of
f(x)=-x^2+3
Range:
(-\infty, 3]
State all 3 versions of the Pythagorean Identity
sin^2(x)+cos^2(x)=1
1+cot^2(x)=csc^2(x)
tan^2(x)+1=sec^2(x)
State the zeros of
f(x)=2x^2+5x+12
x=-4,x=3/2
Evaluate
log_{sqrt(8)}64
4
Find the exact value
cos[tan^(-1)(7/4)]
4/sqrt(65)
State the domain, range, and asymptote equation of:
f(x)=3^x-1
Domain:
(-\infty,\infty)
Range:
(-1,\infty)
Asymptote:
y=-1
Find the nonnegative angle with least measure that is coterminal with
\theta=-(21pi)/4
theta_c=(3\pi)/4
State the equations of the asymptote(s)
f(x)=1/(x-3)
Vertical Asymptote:
x=3
Horizontal Asymptote:
y=0
Solve
5^(x+1)=1/125
Solve \triangle ABC given
a=4,b=9, B=52º
Round to 2 decimal places as needed.
A=20.50º
B=52º
C=107.50º
a=4
b=9
c=10.89
State the domain, range, and asymptote equation of:
g(x)=log_5(x+4)+3
Domain:
(-4,\infty)
Range:
(-\infty,\infty)
Asymptote:
x=-4
Find the exact value of cos(2x) when sin(x)=3/5 and pi/2≤x≤pi .
7/25
State the type and location of any discontinuities for the following function
R(x)=(x^2-4)/(x+2)
The function has a hole (removeable) discontinuity at
(-2,1)
Expand the expression completely using properties of logs:
log_d((a^2b)/c)
2log_d(a)+log_d(b)-log_d(c)
Find the general solutions to 2sin(3x)=\sqrt(2) . Then find all general solutions in [0,2pi) .
x=pi/12+(2pi)/3n, x=(pi)/4+(2pi)/3n
{pi/12, pi/4, 3pi/4, 11pi/12,17pi/12, 19pi/12}
State the intervals for which f(x) is above the x -axis.
f(x)=x^3-x
The function is above the x-axis on the intervals:
(-1,0)\cup(1,\infty)
Find all general solutions. Then provide all solutions in the interval [0,2\pi) .
tan(x)=sqrt3
x=\pi/3+n\pi
x=pi/3,(4pi)/3
A rancher with 180 meters of fence intends to enclose a rectangular region along a river (which serves as a natural boundary requiring no fence). Find the maximum area that can be enclosed.
The maximum area is 4050m2.
Suppose that $2000 is invested in an account that pays interest compounded continuously. Find the amount of time that it would take for the account to grow to $4000 with an APR of 5.75%.
Round to the nearest tenth.
12.1 years
Find the exact value of cos(a+b) given a lies in Quadrant III with sin(a)=-4/5 , and b lies in Quadrant II with cos(b)=-5/8 .
(15+4\sqrt(39))/40