Functions
Rational Expressions & Transformations
Exponential functions
Trigonometry
Trigonometric Functions
100
2/5 is what type of number?
Rational
100
What transformations have been applied to the following function from its base of y=f(x).
y=2f(-3x+6)+2
1. Vertically stretched by a factor of 2
2. Horizontally compressed by a factor of 1/3
3. Reflection in the y-axis
4. Shifted 2 units to the right
5. Shifted 2 units up.
100
The expression (3/4-2/9)^0 is equal to?
1
100
What is the exact value of csc30 degrees?
2
100
What is the amplitude, period, and equation of the axis for the function y=4sin(2x)+10
A=4
Period=180º
Equation of axis: y=10
200
Is this a function? Why? State the domain and range.
No, because it wouldn't pass the vertical line test.
Domain: {x∈R|0≤x}
Range: {y∈R}
200
Given that f(x)=1/x, what is the defining equation of g(x) where g(x)=f(x+1)-5?
g(x)=(1/x+1)-5
200
Simplify the following, state your answer using positive exponents only.
(√x2)(4√x 10)
x7/2
200
Use special triangles and the CAST rule to find the exact value of sec 300º
2
200
What transformations have been applied to the following function from its base of f(x)=sinx.
g(x)=4cos(2x-90)+6
1. Vertically stretched by a factor of 4
2. Horizontally compressed by a factor of 1/2
3. Phase shift 45° to the right
4. Shift 6 units up
300
Simplify (3-√5)(4+√5)
7+√5
300
Simplify the following expression and state the restrictions.
x^2+x-12/x+2 ÷ 4x+16/3x+6
3x-9/4 or 3(x-3)/4
x≠-4, -2
300
For the function y=3(3)3(x+5)-4, determine the domain, range, and the equation of asymptote.
D:{x∈R}
R:{y∈R|y>-4}
Equation of Asymptote: y=-4
300
Determine the value(s) of angle Θ, for cos = -0.8 where 0º ≤ Θ ≤ 360º.
Θ1=216.9º
Θ2=143.1º
300
Sketch one cycle of the function y=3sin[0.5(x+45)]+2
State the domain and range.
D = {x∈R}
R = {y∈R|-1≤y≤5}
400
Find the exact and simplified roots of the function
w(x) = 6x2 - 3x - 3
x=(1±3)/4
400
Find the inverse of the following function.
f(x)=√x -5
f-1(x)=(x+5)2
400
A basketball bounces on the floor, after each bounce, the height of the ball above the floor is given by the equation h=4(0.7)x, h is height of the ball in meters after x bounces.
a) what is the initial height of the ball?
b) what does 0.7 mean in the context of the problem?
c) what is the height of the ball after 7 bounces? round your answer the nearest tenth of a meter.
a) 4 meters
b) it means the height of the ball decreases by 30% after each bounce.
c)0.33 meters
400
Triangle ABC has A=70º, a=12cm, and b=10cm. Is it and ambiguous case? Explain and solve the triangle(s).
It is ambiguous case because it is SSA and it resulted in one triangle.
Triangle (i) has B=51.5º, C=58.5º, and c=10.9cm
400
Prove the identity
tan2x+1/tan2x-1=1/sin2x-cos2x
1/sin2x-cos2x=1/sin2x-cos2x
500
A smoothie company is selling their smoothies for $3.50 each. At this price, they sell about 200 smoothies per day. The company's employees predict that for every 10 cent decrease in price, the sales of smoothies will increase by 20 smoothies per day. Solve for the smoothie price that will maximize the company's revenue.
the smoothie price that will maximize revenue is $2.90
500
Determine the coordinates for the image based on the given description of the transformations.
original point (f(x)): (-4, 3)
transformed function: 4f(x-2)+2
-2, 14
500
The radioactive isotope radium-226 has a half life of 800 years. A sample of the radium has a mass of 100mg, what would the mass be after 5000 years?
1.31mg
500
Nico is standing in front of a building at a small urban complex, ready to walk to another building a few blocks away. The complex is designed so that its main pathway faces north toward a tall building. From the starting point of the pathway, the angle of elevation to the top of the tall building is 7°. From a point 500 meters perpendicular to the pathway, the angle formed by the starting point of the pathway and the tall building is 60°. What is the height of the building?
122.8m
500
James gets on a Ferris wheel and is 4 meters from the ground. When he is at the top of the ride, he determines that the height from the ground is 28 meters. He also ensures that it takes 120 seconds for the wheel to make one rotation. Determine a cosine function to model James's height above the ground and sketch 2 rotations of the ride.
y=-12cos3x+16
