Functions (domain, range, and comp.)
Functions
and their inverses
Functions
transformations
Exponents
Logarithms
100
y=a(x+2)(x-3) 4=a(0+2)(0-3) 4=a(2)(-3) 4=a-6 /-6 -2/3=a
What is a function that has the x-intercepts of -2 and 3 and a y intercept of 4?
100
The function is one to one
What is a quality a function needs to have in order to have an inverse?
100
f(x)=x^2
What is the parent function of a parabola?
100
an example of this exponential rule is you have x people in y rooms
What is (a^m)^n
100
given b>0 but not equal to 1 y=b^x is the same as logb(y)=x
What is the definition of a log?
200
(0,0) (2,0) are the zeros of this function
What is f(x) = -(x -1)^2+1?
200
The dependent and independent variables are switched
What is the relationship between an inverse and its original function?
200
moves the parabola 5 to the right and 2 down
What is f(x)=(x-5)^2-2
200
relies on previous term and initial value
What is a recursive sequence?
200
10^x=3
What is log10(3)=x?
300
when the output values of one function become the inputs of a second function
What is the composition of a function?
300
solve for x and then switch the x and y and write the new equation f^-1(x)
What is the process in which you find the inverse function?
300
x=2^y (1,1) (4,2) (8,3) (16,4)
What is the inverse of y=2^X and what are four points on the graph?
300
y=1000(1.03)^x after two years y=1000(1.03)^2 1060.9
What is exponential growth?
300
it is why log3(30)=log3(3)+log3(10)
What is log(ab)=log(a)+log(b)
400
an imaginary line the equation approaches but never touches
What is an asymptote?
400
f^-1(x)=(x+5)/3
What is the inverse of f(x)=3x-5
400
limit the domain so its #>0 {0, oo)
What is a way to make a parabola have an inverse that is also a function?
400
8^2x=2^x-1 2^3(2x)=2^x-1 6x=x-1 5x=-1 x=-1/5
What is x?
400
logs are exponents so 3^4 equals 64
What is the reason log (64) is three times log (4)?
500
the domain becomes the new range and the range becomes the new domain
What is the relationship between the domain and range of the original equation and its inverse?
500
f(x) =x^1/2 g(x) =(x+1)/2 ((x+1)/2)^1/2)
What is f(g(x))?
500
x=y
What is a line you can draw on a graph to judge if two equations are inverses?
500
f(X)=b^x 1^x will always equal x 0^x will always equal 0
What is the reason we do not consider b = 1 or b < 0?
500
5^x = 15 log5(15)=x x=25 log(x)/log(5)=log5(25)
What is a way to change the base from 10 to five on our calculator given the equation 5^x=15?
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