Show:
Exponents
Logarithms
Inverses
Transformations
Domain, Range and Compositions
100
y=a*1/2^x
What is the half life equation?
100
Log(10,x)=y
What is the common logarithm base?
100
Horizontal line tests
What is the easiest way to see if a function is an inverse?
100
F(x)=1+3^(x/3)
What is f(x) moved up 1 and stretched horizontally by 3?
100
Domain: The values that can be imputed into a function Range: The values that are the product of the functions
What are the definitions of Domain and Range?
200
log(b,y)=x
How do you write b^x=y as a logarithm?
200
Given that b>0 and b≠1 y=b^x if and only if log(b,x)=y
What is the definition of a logarithm?
200
For every x value there is one y value and for every y value there is one x value
What condition must be met in order to have an inverse function?
200
F(x)=3^x F(x)=4(3^x+6)
What is f(x)=3^x stretched vertically by 4 shifted left by 6?
200
g(x)=-4(x) stretches the range by 4 and reflects the function of the y axis does not effect the domain
What is the relation of -4 of g(x)=-4(x) have with the domain and range of the function
300
a^m*a^n=a^m+n (a^m)/(a^n)=a^m-n (a^m)^n=a^mn a^-n=1/a^n
What are four basic properties of exponents?
300
Log(x)/Log(b)=Log(b,x)
What is the formula for finding non-common base logarithms?
300
f(x)=3√x cubed root of x 8,2 27,3 29.791, 3.1 64,4 125,5 140.608, 5.2
What is the inverse of f(x)=x^3
300
f(x) = 3^x moved left 1 stretched horizontally by 3 stretched vertically by 2 flipped over the y axis moved up 4
What is g(x) = -2(3^(x+1)/3)+4
300
f(g(h(x)))=2^5/x-6
If f(x)=2^X, g(x)=5x-6, h(x)=1/x then what is f(g(h(x)))?
400
STAT-EDIT-QUIT-STAT-CALC-EXPREG
How do you find the exponential line of best fit on a calculator?
400
All numbers> 0 to the 1st power are themselves All numbers except zero to the 0 power is 1
What are the properties of logarithms?
400
y=1/3x+2
What is the inverse of y=3x-6
400
F(x)= 3^x Flipped over the x axis Stretched vertically by 2 Moved up 4 Stretched horizontally by 3 Moved left 1
What is g(x)=2(-3^x/3+1)+4
400
The domain of function f is [-4,8] and the range of function f is [-5,6] The domain of function g(x)=f?(x?) is [-8,16] and the range of function f is [-15,18]
What is the domain and range of function f and g(x)=3f(x/2)
500
X-axis
What line on a graph does the basic exponential function never touch?
500
b^x=y
What is the equivalence of a logarithm exponentially?
500
f(x)=3√(-5+x)/6
What is the inverse of x=-6y^(3)-5
500
f(x)=3^x F(x)=-1/2(6^x-16)-6
What is f(x)=3^x reflected over the y axis, shrunk vertically by 2, shrunk horizontally by 3, shifted right by 16, moved down 6
500
f(g(h(x)))=8^(5/(x-5)-6))-2
If f(x)=8^X-2, g(x)=5x-6, h(x)=1/x-5 then what is f(g(h(x)))?