Show:
Functions: Domain, Range, Composition
Functions: Inverses
Functions: Transformations
Exponents
Logarithms
100
The possible x values of a function
What is the domain?
100
y=x^2+6 x=y^2+6
What is the inverse?
100
f(x)=2^x transformed to f(x)=2^3x
What is horizontal squeeze by a factor of 1/3?
100
(-2, 1/9) (-1, 1/3) (0, 1) (1, 3) (2, 9) (3, 27)
What are some points of f(x)=3^x?
100
The inverse of an exponential function
What is the log function?
200
The test to figure out if something is a function or not
What is the vertical line test?
200
The line that you flip a function over to find the inverse of the function
What is the y=x (the origin)?
200
Negative on the outside of the function f(x)=-x^2
What is reflecting over the x axis?
200
1/a*a=1 a^1*a^-1=a^0=1
What is the justification of a^-1=1/a
200
log(100000000000)
What is 11?
300
The x intercepts. To find them set y to 0 and then find the point where it touches the x intercept, which is (x,0)
What are zeros?
300
Switching the x and y points
How do you find the graph of the inverse of a function?
300
original: f(x)=lxl f(x)=-l-xl-1
What is the equation of the absolute value function after it's been reflected over the x and y axes and shifted down 1?
300
f(x)=a*b^x : b is less than 1 and greater than 0
What is exponential decay?
300
log(4)+log(10) hint: not actual answer but another way of writing it
What is log(40)?
400
For each output there is EXACTLY one input
What is a one-to-one function?
400
It is a function that undoes another function
What does the inverse do?
400
Original: g(x)=x g(x)=1/2(-1/5x)
What is the linear function g(x), reflected over the y axis and horizontally stretched by a factor of 5 and vertically shrunk by a factor of 1/2?
400
For an explicit sequence you can plug in any value to find that term in the sequence, but for recursive you need the preceding term each time.
What is the difference between an explicit sequence and a recursive sequence?
400
log(b,x^y)=y*log(b,x)
What is the log power rule?
500
A function that is symmetrical across the x axis f(-x)=f(x)
What is an even function?
500
There cannot be an inverse unless you limit one side
What is inverse of a non one-to-one fumction?
500
Original: f(x)=x^2 f(x)= 2(4x^2+6)-3
What is function x^2 vertically stretched by a factor of 2, horizontally shrunk by a factor of 4, shifted left 6 and down 3?
500
Jacket start price: 202 dollars Time is in weeks Equation: y=202*.94^3
What is the equation for the price of a jacket in 3 weeks that decreases in price each week by 6% each week?
500
log(b,x)= log(k,x)/log(k,b)
What is the change of base formula?