Exponential and Logarithmic Functions
What does h represent in an exponential functions?
Horizontal Shift
Simplify:
(3x5) (5x2)
15x7
6k-36/k-6
6
45/45/90 triangle
hypotenuse = y, legs = x
x=10
y=?
10 sqroot (2)
Convert to degrees:
10pi/18
100 degrees
Write this equation in exponential form:
log3 9 = 2
32 = 9
Simplify the radical:
2 3sqroot (648)
12 3sqroot (3)
6x2y3/2x2y2 * 10x3y4/18y2
5x3y3/3
What is the reciprocal of Sine?
Cosecant
Convert to radians:
225 degrees
5pi/4
Write this equation in logarithmic form:
142 = 196
log14 196 = 2
Divide and rationalize. Answer in simplified radical form:
3 sqroot (12)/ 4sqroot (7)
3 sqroot (21)/ 14
Add:
x2+5x+6/x2-4 + 2/x-2
x+5/x-2
x doesn't equal 2
Find x,y,z
90degree/18 degree/z
hypotenuse = 34, LL = x, SL = y
x= 32.34
y= 10.51
z= 72 degrees
Find the 4 points for this equation:
f(x)= 3x+6/x+3
3/2, 0, 6, 4.5
Solve:
74x+11 =1/7
x=-3
verify that f(x) and g(x) are inverses:
f(x) = x+7 and g(x) = x-7
x-7+7=x
x+7-7=x
Divide:
x/x+2 / 1- w/w+2
w/2
An airplane flying at 20,000 feet is heading toward an airport. The airports landing system sends radar signals from the runway to the airplane at a 50-degree angle of elevation. How many miles along the ground is the airplane from the runway?
x=16781.99 feet
What quadrant is this in:
sin 19pi/3
Quadrant 1
Solve and check for extraneous solutions:
log3 (4x+8) -7 = -3
x=18.25
81>0
Find f(g(x)):
f(x) = x2 and g(x) = sqroot (x)
X
Divide complex fractions:
2x2-2x-40/3x+ 12 / x3-5x2/9x2+36x
6(x+4)/x
x doesn't equal 0
A ten foot ramp is used to unload furniture from a truck. If the back of the truck sits 3 feet above the ground, find the measure of the angle makes with the ground.
x= 17.46
Name all of the transformations:
-3 sqroot (x-2) +1
Right 2, Up 1
Vertical Stretch (factor of 3)
Reflection (over 1)