Changing & Combining Functions
Let f(x)= x2. Shift the graph right by 2 then up by 3. What is the formula of the new function?
(11)
g(x)= (x - 2)2 + 3
Find the inverse function for f(x)= -3 / (2x + 5).
(10)
invF(x)= (-3 / 2x) - (5 / 2)
Use properties of logarithms to combine the following expressions into one logarithm.
ln(2) + (1/2)ln(x-1) - 2ln(x)
(8)
ln[ (2)sqrt(x-1) / x2 ]
Let f(x) be an odd function. The points (1,2) and (-3,4) are on the graph f(x). Find the value of f(-1) + f(3).
(6)
-6
Let f(x)= |x|. Shift the graph of f(x) right by 2 then down by 3. What is the new function?
(3)
g(x)= | x - 2 | - 3
Rationalize the denominator.
2 / sqrt(3) + 1
(9)
sqrt(3) - 1
How much money would you accumulate if you invested $6000 at 4% interest compounded continuously for 20 years?
(19)
$13,353.25
Solve the equation and round your answer to the nearest four decimal places.
72x - 11 = 0
(17)
0.6161
Evaluate the quantity A= f(1) + f(2) + f(3) where the function f(x) is defined as follows:
f(x)={ 2x - 1 x </= 2
x2 - 3x + 1 x > 2
(2)
5
For f(x)= x2 - 2x - 10 and g(x)= sqrt( 5x + 1 ), evaluate (f o g)(3).
(4)
18
Find the inverse function for f(x)= (4x - 2) / (x - 1).
(15)
invF(x)= (x - 2) / (x - 4)
Solve the logarithmic equation:
log(x) + log(x - 15) = 2
(7)
x= -5, 20
Find the center and radius of the circle. Then graph.
( x - 2 )2 + ( y - 9 )2 = 81
(2--3)
center: (2,9)
radius: 9
For f(x)= x2 - x + 1 and g(x)= sqrt(3x - 1), evaluate (f o g)(1).
(14)
3 - sqrt(2)
Find the inverse function of f(x)= 2 / ( x + 1 ).
(5)
invF(x)= ( 2 / x ) + 1
Find the exact solution of the equation:
5e3x+1 = 50
(18)
(1/3)ln(10) - (1/3)
Solve the equation:
(1 / 9)-2x + 3 = 3x+5
(12)
x= (11 / 3)
Evaluate the quantity A= f(1) + f(3) where the function f(x) is defined as follows:
f(x)= { sqrt(2x - 1) x </= 2
x2 - x + 1 x > 2
(16)
8
Find the value of the following function given
f(x)= 2x + 1 and g(x)= 3x + 5
f(g(f(g(f(g(f(2)))))))
1553
Given the following function, find the difference quotient [ f(x+h) - f(x) ] / h
f(x) = -3x2 + x + 7
(1)
-6x -3h + 1
Use the properties of logarithms to write the following expression as a sum or difference of simple logarithmic terms.
ln[ (x - 3) / (2)cbrt(x) ]
(20)
ln(x - 3) - ln(2) - (1/3)ln(x)
How much money would you have if you invested $2000 at 5% interest compounded monthly for 50 years?
(13)
$24,238.77
Find the inverse of f(x)= (2x + 3) / (x - 1).