Domain, Range, Compositions
Inverses
Transformations
Exponents
Logarithms
100
all possible Y values of a function
what is range?
100
f^-1(x)
What is the notation of the inverse of a function?
100
y=x was vertically shifted up three
What is the transformation that was performed on: y=x -------> y=x+3
100
the number of times a number (the base) is multiplied by itself.
What is an exponent?
100
Given b>0 & b≠1 y=b^x iff log b (y)= x
What is the definition of a logarithm?
200
Domain= (-∞,∞) and Range= (-∞,∞)
what is the domain and range of y=x / y=x^3 ?
200
horizontal and vertical line test
what is one method for determining if a function is one to one?
200
the movement of any point by a fixed distance.
What is a transformation?
200
the time in which a substance decays to half its mass.
What is a half life?
200
log b (b) = 1 log (a) +log (b) = log (a+b) log b (1)=0
What are some of the properties of logarithms that we have covered
300
Domain is all real numbers ≠ 0 Range is all real numbers ≠ 0
What is the domain and range of the inverse function/ f(x)=1/x)
300
y=x
What line is the inverse of a function reflected over?
300
f(1/2x)^2 or f(2x)^2
What is a horizontal dilation?
300
√x^2=(x^1/2)^2=x^1=x
What is the difference between √x and x^1/2 ?
300
5^3=125 is the exponential form
what is the exponential form of log5 (125)=3 ?
400
the output values of one function become the inputs of a second function.
What is a compositions of two functions
400
switch the x and y values and solve for y
What is the way to solve for a function's inverse
400
original: f(x)=3^x transformed: f(x)=5(3^(x+2))
What is the equation for the function f(x)=3^x transformed by a horizontal shift of 2 to the left and a vertical stretch of 5
400
a^-1=a^0-1=a^0/a^1=1/a
What is the justification for the rule: a^-1=1/a
400
log b (1)=0 -> b^0=1
what is the justification for log b (1)=0
500
f(x)=3x^2, g(x)=(4x): 48x^2
What is f(g(x))?
500
one to one
what is the one thing a function must be inorder to have an inverse
500
y=-|3x|+3
What is a vertical shift of three, a vertical flip and a horizontal squeeze by a factor of three on a absolute value function?
500
a^m*a^n= a*a*a*a... * a*a*a*a*a... m # of times <> n # of times = a*a*a*a*a*a*a*a*a*a*a*a*a... m + n # of times
What is the justification for the rule a^m * a^n = a^m+n ?
500
log 3(243) = log3 (9*27) = log3 (9) + log3 (27) = 2+3 = 5
What is the justification for log(a*b) = log (a) + log (b)
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