Rational Functions
Describe the transformations of
f(x)=1/x to 1/(x-4)+2
Right 4, up 2
What are the new coordinates of the key points and asymptote of:
f(x)=2^(x+3)-4
(-3,-3), (-2,-2), y=-4
What is the VA of:
log_(1/2)(x+3)-4
x=-3
Convert to degrees:
pi/3
60 degrees
Find an angle coterminal with 50 degrees
410 degrees
Determine the vertical asymptote(s) of
(x^2-4x+3)/(x^2+x-2)
x=-2
Solve for x:
3^(2x)=27^(x+5)
x=-15
What are the new coordinates of the key points and the vertical asymptote of:
f(x)=log_3(x) to g(x)=-log_3(x)+2
(1,2), (3,1) and x=0
Identify the quadrant:
(15pi)/4
IV
Find an angle coterminal to
(5pi)/12
(29pi)/12
Determine the point of discontinuity (hole):
f(x)=(x+5)/(x^2-25)
(2,0)
Find the exact value of x
4^(2x-1)-5=20
(log_4(25)-1)/2
Evaluate:
2e^(ln(7x))
14x
Identify the quadrant given
tan theta=-2/7 and cos theta>0
IV
Find the exact value of
cos(pi)
-1
Determine the x-intercept(s):
g(x)=(x^2-5x-14)/(x+1)
(7,0) and (-2,0)
Find the exact value of x:
e^(2x)-9e^x-10=0
ln(10)=x
Solve for x:
2log_4(x)=log_4(36)
x=6
Given cos(x)=-3/5 and tan(x)>0 find sin(x)
sin (x)=-4/5
Find the exact value of
sin(-pi/4)
-sqrt2/2
Determine the horizontal and vertical asymptotes of
f(x)=(-2x^2+5x+3)/(x+1)
Horizontal: None
Vertical: x=-1
Calculator: In Fayette County, Kentucky the population continuously grew from 260,512 people in the year 2000 to a population of 268,080 people in the year 2005. Use the equation A(t)=A_0e^(kt) to write a function modeling this situation.
A(t)=260512e^(.006t)
Solve for x:
log_2(x)+log_2(x-7)=3
x=8
Calculator: You are taking your first hot air balloon ride. Your friend is standing on a level ground 100 feet away from your point of launch and records your ride. At one instant, the angle of elevation from the phone to your face is 31.7 degrees. One minute later the angle of elevation if 76.2 degrees. How far did you travel, to the nearest tenth of a foot?
345.3 feet
Find exact value of
sec^2(pi/3)/tan((5pi)/6)
-4sqrt3