Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
57 Cards in this Set
- Front
- Back
What is bigger 10^x or x^10?
|
10^x, initially x^10 is bigger, but as they increase 10^x will overtake x^10
|
|
Define exponential decay.
|
when get the graph is getting smaller and smaller (opposite of exponential growth)
|
|
What indicates that a exponential expression's graph will be a exponential decay?
|
If the exponent is negative, or base is between 0 and 1
|
|
Give two examples of exponential expressions that would result in a decay.
|
3^(-x) and/or 0.15^x
|
|
Give an example of a exponential expression that would result in a exponential growth.
|
5^x
|
|
Draw an example of a exponential decay and growth graph.
|
http://www.google.com/imgres?imgurl=http://fym.la.asu.edu/~tturner/MAT_117_online/Exponential_Functions/decay_e%255E-x.gif&imgrefurl=http://fym.la.asu.edu/~tturner/MAT_117_online/Exponential_Functions/Exponentials.htm&usg=__LzyfOOLqw0_z-mJEQVpOOqWFiaw=&h=486&w=486&sz=12&hl=en&start=11&sig2=58ZQrrjPaLwfJS6oPG8FMA&zoom=1&tbnid=yTYwgck0D-0-bM:&tbnh=150&tbnw=150&ei=rigITp3iD4uDtgfsvbGwDQ&prev=/search%3Fq%3Dexponential%2Bdecay%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26sa%3DN%26rls%3Dorg.mozilla:en-US:official%26biw%3D1252%26bih%3D496%26tbm%3Disch&um=1&itbs=1&iact=hc&vpx=140&vpy=172&dur=590&hovh=150&hovw=150&tx=154&ty=121&page=2&ndsp=10&ved=1t:429,r:5,s:11&biw=1252&bih=496 (decay)
http://www.google.com/imgres?imgurl=http://www.adambreckler.com/wp-content/uploads/2009/08/exponential_growth_520.jpg&imgrefurl=http://www.adambreckler.com/the-impact-of-exponential-growth&usg=__uo4zfOm1JRlU3aGwLIuE55j-9M0=&h=520&w=629&sz=89&hl=en&start=3&sig2=SZWLPfhsoYDG1ABQhLyDDw&zoom=1&tbnid=7sMTi8lEQ2V2aM:&tbnh=113&tbnw=137&ei=-CgITrCODNKXtwfcppjFDQ&prev=/search%3Fq%3Dexponential%2Bgrowth%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26sa%3DN%26rls%3Dorg.mozilla:en-US:official%26biw%3D1252%26bih%3D496%26tbm%3Disch&um=1&itbs=1 (growth) |
|
What type of graphs do logarithmic functions resemble?
|
square root graphs
|
|
True or False:
Logs are the inverse of exponents. |
TRUE
|
|
True of False:
The graphs of 2^x and log2(x) are inverses. |
TRUE
|
|
What does a composite function look like? Or how can you identify that a function is a composite function.
|
g o f (x) and/or f o g (x)
|
|
Translate f o g(x) into a parenthetical form.
|
f(g(x))
|
|
How can you determine that a function is an inverse of its parent function?
|
The x and y coordinates of the inverse will be switched in comparison to the parent function.
ex. parent function (6,3) inverse function (3, 6) |
|
Find the inverse of y=3x+6, writing out the steps as you go.
|
1) write out original equation
2) solve original function for the un-isolated variable (in this example it is x) ex. y-6/3=x 3) now switch the x and y of the equation created in step 2 ex. x-6/3=y 4) you have now found the inverse |
|
What test can be used to determine that a graph cannot have an inverse?
|
Horizontal Line Test
|
|
What type of functions don't have inverses?
|
quadratic functions
ex. f(x)= x^2+4x-3 |
|
How can you algebraically find if a function has an inverse or not?
|
If you cannot isolate x, which is what happens in quadratic equations
|
|
What is the trig identity for csc(x)?
|
1/sin(x)
WTR: Corey Skillfully Creates SINES |
|
What is the trig identity for tan(x)?
|
sin(x)/cos(x) or 1/cot(x)
WTR: Tommy Stole Cookies |
|
True or False:
tan(x) and cot(x) are inverses or eachother |
True
|
|
Due to the fact that csc(x) and sin(x) are inverses, what is sin(x)'s trig identity?
|
1/csc(x)
|
|
What is the inverse of cos(x)?
|
sec(x)
|
|
True or False:
cos(x) and sec(x) are inverses |
True
|
|
What is the trig identity of cos(x)?
|
1/sec(x)
|
|
True or False:
cos(-x)= 3cos(x) |
False, this cos(-x)= -cos(x). This rule also applies for sin(x) and tan(x).
|
|
What is pi equal to in degrees?
|
180 degrees
|
|
Describe the movement of a sine graph (for one period).
|
axis to maximum to axis to minimum
|
|
3sin(x-2)+6=f(x)
Tell the amplitude, period, phase shift, and vertical shift of this function. |
amplitude=3
period=360 (coefficient of x is 1) vertical shift=6 phase shift=2 units to the right |
|
Describe the graph of a regular cosine graph.
|
maximum to axis to minimum to axis to maximum
|
|
What does a negative amplitude suggest about a sine or cosine graph?
|
The graph is inverted.
|
|
Describe the shape of a tan(x) graph.
|
Three graphs, first is a upright half parobola (right) starting at 0 degress, second is an s-shape at 180 degrees, and the final is a inverted half parabola (left) at 360 degrees
|
|
For triangle problems, what is important to remember?
|
SOHCAHTOA
|
|
When you see "arc" in from of tan(x), sin(x), cos(x), csc(x), sec(x), and cot(x) what does it mean?
|
it is the inverse of that particular trig function
|
|
Change arccos N= θ into non-inverse form, include the steps.
|
1) isolate the N, by moving the arccos next to the θ
ex. N= arccos θ 2) remove the "arc" from the arccos ex. N=cos θ 3)you are finished |
|
How do you remember the unit circle?
|
1) learn your quadrants and the signs that go with it.
2) the coordinates of the point closest to the x-axis will always be: (±√3/2 , ±1/2) 3)the coordinates closest to the y-axis will always be: (±1/2 , ± √3/2) 4)the coordinates in the middle will be: (± √2/2 , ± √2/2) 5) the radians that go with (± √2/2 , ± √2/2) go in intervals of 1/4 (make sure to include ╥ in the numerator) 6) the radians of the y and x axis go by 1/2 (make sure to include ╥ in the numerator) 7) |
|
Rewrite this problem:
Evaluate arcsin √2/2. |
√2/2 is the sine of what angle?
|
|
True or false: the ranges of arcsin(x) and arctan(x) are the same.
|
True
|
|
True or False:
Sine applies to x-axis |
False, y-axis
|
|
What axis does cosine apply to?
|
x-axis
|
|
What is the quadratic equation?
|
-b ± √b²-4ac/2a
|
|
True or False: A function can have more than one output (y-value) for each input (x-value).
|
FALSE
|
|
For functions, what is the x-value called and what are the y-values called?
|
x-value=domain
y-value=range |
|
When given the graph of a function, how can you determine whether or not it is a function?
|
Vertical Line Test
|
|
What is another name for a rational expression?
|
polynomial fraction
|
|
√x= -3
True or False? |
False
|
|
(x²)^4= x^8
|
True
|
|
True or False:
(x^3)(x^5) = x^15 |
False, it is x^8
|
|
True or False:
(x/y)²=x²/y² |
True
|
|
Solve: (x²y^3)^0=?
|
1, anything to an exponent of 0 will equal 1
|
|
What is √4 in exponent form?
|
4^½
|
|
What is the circumference formula?
|
2πr
|
|
What is the formula to determine the area of a circle?
|
A=πr²
|
|
When is a quadratic graph "skinny"?
|
when a>1
ex. when a=9, the quadratic will be skinny WTR: higher the number the skinnier it is |
|
When is a quadratic graph "fat"?
|
when a<1
ex. when a=½ the quadratic will be fat WTR: the smaller the number the fatter the graph |
|
What point is the vertex?
|
(h,k)
|
|
Write out vertex form of a quadratic equation?
|
a(x-h)²+k
|
|
What is the formula for velocity?
|
v=d/t
|
|
sin²(x) + cos²(x)=?
|
1
|