Transformations
In g(x) = a f (b(x - h)) + k, what do a, b, h, and k do?
a = a vertical stretch/compression
b = a horizontal stretch/compression
h = a horizontal shift
k = a vertical shift
Can a function be BOTH even and odd? Can it be NEITHER even or odd?
No, a function can't be both even and odd, BUT it can be neither.
Give a real life example of something that might be measured as a periodic function.
- Ferris Wheel Rotations
- A Heartbeat
- Sound Waves
- Light Waves
- Ocean Tides
- etc.
What does SohCahToa stand for, and when can we use it?
Sin = opp/hyp, Cos = adj/hyp, Tan = opp/adj
We can use it when working with right triangles!
What is the equation for Arc Length?
S = rθradians
In g(x) = a f (b(x - h)) + k, what variables effect the x-values of your points (out of a, b, h, and k)?
The variables b and h.
What equation do you use to test if a function is even? What about to test if it's odd?
To test if it's even you use the equation: f(x) = f(-x)
To test if it's odd you use the equation:
f(-x) = -f(x)
max = highest point on a periodic function
min = lowest point on a periodic function
amplitude = distance b/w midline and max OR midline and min
period = # of units required for the pattern to repeat
midline = the middle of the graph
When looking at the exact value for cos (θ) of an angle that is on the unit circle, do we look at the x-value or y-value of the corresponding point?
The x-value! Remember, when you see cos think x, and sin think y.
Convert 161º to radians.
161º = 2.81 radians
Given the function f(x) = x2, describe how you would transform it to create the function g(x) = (x - 3)2.
Apply a horizontal translation of 3 units to the right.
If a function is even, it has "y-axis symmetry". Can a function have "x-axis symmetry"? Why or why not?
A function can NOT have x-axis symmetry because then it wouldn't pass the vertical line test, meaning it is not a function.
Draw a periodic function and label the following parts: amplitude, period, maximum, minimum, and midline.
Let's see it!
Solve for θ in degrees: sin(θ) = 22/29
θ = approximately 49.34º
Let's check and talk about it!
Given the logarithmic function
g(x) = log2(x). Describe how you would transform it to create the new function
h(x) = -log2(x + 1) + 3.
Apply a reflection over the x-axis, a horizontal translation of -1 unit to the left, and a vertical translation of 3 units upward.
It is even because it has y-axis symmetry!
Given the function
f(x) = 3sin(x), determine its amplitude.
The amplitude is 3.
Solve: cos(60°) + sin(30°) - tan(45°)
= (1/2) + (1/2) - 1
= 0
θ is between 0 and 2pi. What values of θ give
sin(θ) = -1/2?
7pi/6 and 11pi/6
Given the cubic function f(x) = x3, how would you transform it to create: h(x) = -2(x + 1)3 - 4?
Reflect about the x-axis, apply a vertical stretch by a factor of 2, a horizontal translation of 1 unit to the left, and a vertical translation of 4 units down.
Is the following function even, odd, or neither?
f(x) = 3x2 +4x -5
Neither!
f(-x) = 3x2 - 4x -5
-f(x) = -3x2 - 4x +5
A ferris wheel, with a 100m radius, stands on a platform that is 5m in height. 1 revolution of the wheel takes 8 minutes. Draw a periodic function to represent this ferris wheel and its revolutions.
Let's check it out!
If a circle is centered at the point (-4, 3) and you are given r = 7.8 as well as θ = 40º, what are the coordinates of point P?
Point P is located at approximately (1.975, 8.014).
What is the radius of a circle if θ = 119º and S = 7.7?
Remember to convert to radians first!
119º = 2. 07694 radians
Then use your equation to find that
r = 3.71