Functions
What are the domain and range and determine if its a function
E = {(2,1),(5,4),(-3,-1),(7,3),(-1,8)}
D : {-3,-1,2,5,7}
R : {-1,1,3,4,8}
Is a function
List the transformations of the following equation
f(x) = 4x-5 - 4
- 5 units rights
- 4 units down
What is the amplitude and period of the function y = -7cos3x
Amplitude = 7
period = 1200
If an angle measures 4300, what is its coterminal angle between 0 and 360 degrees.
500
How much interest earned if $3000 is invested with a rate of 8% per annum for 5 years
$1200 interest earned with a total of $4200
State 2 ways to restrict the domain of this equation
f(x) = (x + 7)2 + 3
AoS = -7
D: {xeR| x > or equal to -7}
D: {xeR | x < or equal to -7}
Simplify (x5/3) (x2/5)
(15/----x)31
A cosine function reflects across the x-axis, VS by a factor of 2, HC by a factor of 3, shifts 1200 right, 2 units up
y = -2cos[3(x-1200)] +2
Triangle with sides a=8.9cm, b = 7.4cm, c = 9.2cm. Find angle A
640
$5000 is compounded annually at a rate of 5%. What is the amount after 10 years?
$8144.47
If f(x) = 3- 5x, find and simplify 2f(n -3)
-10n + 32
A bacteria triples in number everyday for 7 days. There are currently 50 bacteria in the sample population. Determine an equation to model the growth of population
P(d) = 50(37)
For the function f(x) = 4sin(3x - 15) - 10, state the period, amplitude, equation of axis, and phase shift.
4sin[3(x-5)] - 10
Period = 120
Amplitude = 4
Equation of axis : y=-10
Phase shift = 5 right
state the 3 primary trig ratios with the point (-7,-3)
sinx = -3 / /-----58
cosx = -7 / /-----58
tanx = 3 / 7
How much money should be invested to have $200 000 after 15 years with an interest rate of 4% compounded monthly?
$109 890.11
Write the inverse for the function f(x)= 3x + 5
f-1(x) = x - 5 / 3
A bacteria doubles its population every 5 minutes. It initially has a population of 500. How much bacteria will there be in 0.5 hours?
512 000 bacteria
The max height of the ferris wheel of 20m is reached in 20s, then the minimum height of the 1m at 150s.
Make an equation for the function
State the 3 reciprocals trig ratios for the point (-7,-3)
cscx = -3/--58 / /--58
secx = -7/--58 / /--58
cotx = 3/7
If $250 is deposited every 6 months with an interest rate of 9% compounded semi annually. How much money is there after 7 years?
$4733.33
consider h(x) = 5x + 3 as well as f(x) = x2 + 2x - 2
Simplify 3f(x) + h(-x)
3x2 + x - 3
The half life of calcium is 15 years. For a 180mg sample, how long will it take to decay to 20% of its original amount?
34.8 years
Prove: sec2x + csc2x = sec2x x csc2x
1/cos2x x 1/sin2x
LS = RS
2 buildings are 15m apart from each other. The distance from the top of the taller building to the shorter building is 20m. the angle of depression from the top of the shorter building to the base of the taller building is 650. How tall is the taller building.
45.21m
A savings account is opened to have $7500 after 4 years. A deposit is made every moth with an interest of 6.5% compounded monthly. How much are the deposit in the account?
The deposits should be $137.29 every month