What transformations were made on the following function (compared to the basic function)?
h(x)=-log (x-1) +2
2
right 1 unit
reflect across x-axis
translate up 2 units
100
Write a new equation so it shows the following transformations f(x)=2^x
-3 units to the right
-5 units down
-stretch by factor of 3
f(x)=3(2^(x-3))-5
100
Find the domain: f(x)=x^2+4
(-inf,inf)
200
What is sin(5pi/4)?
-sqrt(2)/2
200
sin^-1(sin(5pi/6)) = ?
pi/6
200
Solve log 32
2
5
200
Is 6x^-4 an exponential function?
no
200
Is the following function even, odd or neither?
f(x)=sqrt(x^2 +2)
even
300
Convert from decimal form to DMS
99.37*
99*22'12"
300
cos(2sin^-1(1/2))
1/2
300
Solve- ln(3x+4) - ln(2x+1) =5
-0.4915
300
Find the value of f(x) when x=4, 0, and -3
f(x)=2^x
f(4)=16
f(0)=1
f(-3)=1/8
300
Find the horizontal and vertical asymptote for
q(x)=(x-1)/x
y=1
x=0
400
Find tan(x) and sec(x) if sin(x)=-2/5 and cos(x)>0
tan(x)=-2/sqrt(21)
sec(x)= 5/sqrt(21)
400
From a point 100ft from its base, the angle of elevation of the top of the Arch of Septimus Severus in Rome, Italy, is
34*13'12". How tall is this monument?
68.01ft
400
Find the inverse
p(x)=3log (x-5) + 4
2
p^-1(x)=2^(x-4/3) +5
400
Describe how to transform the graph of f(x)=e^x given the following functions
1- g(x)=e^2x
2- h(x)= e^-x
3- k(x)= 3e^x
1- horizontally shrinking the graph by a factor of 2
2- reflecting of the y-axis
3- vertically stretching the graph by a factor of 3
400
Find f^-1(x)
f(x)=2x+3
f^-1(x)=(x-3)/2
500
State is amplitude, period, phase shift and vertical translation of the function. (relative to the basic function)
y=5cos(3x-(pi/6))+0.5
amplitude- 5
period- 2pi/3
phase shift- pi/18
vertical translation- 1/2 units up
500
sinx sinx
_____ - ______
cot^2x cos^2x
-sinx
500
Write in log form
2^x=3
log 3=x
2
500
Determine a formula for the exponential function whose values are given
x f(x)
-2 6
-1 3
0 3/2
1 3/4
2 3/8
f(x)=3/2 x (1/2)^2
500
Divide f(x) by d(x)
f(x)=3x^4 -5x^3 -2x^2+3x -6
d(x)=3x+1