Functions: Domains, Ranges, Compositions
Functions: Inverses
Functions: Transformations
Exponents
Logarithms
100
If the range of a function is limited then the domain of the function is also limited.
What is how is the range of a function affected if the domain of the function is limited
100
Only one-to-one functions have inverses
What is the distinguishing factor of functions that have inverses
100
f(2x)
What is the equation if you squeeze f(x) horizontally by a factor of 2
100
a^-n = a^0-n = (a^0)/(a^n) = 1/(a^n)
What is the justification for a^-n = 1/(a^n)
100
log(ab) = log(a) + log(b)
What is log(ab) equal to?
200
One possible pair of fuctions for f and g are f(x) = 3x and g(x) = x - 1 if f(g(x)) = 3(x-1)
What is one possible pair of fuctions for f(g(x)) = 3(x-1)
200
f-1(x) = 1-x
What is the inverse function of f(x) = x-1
200
given f(x) f(ax) = a horizontal squeeze if a>1 or horizontal stretch if 0<a<1
What is the type of transformation of f(ax) if a>1 or 0<1<1
200
3^3(x) = 3^6 3(x) = 6 x = 2
What is a solution for 9^x = 3^6
200
Log(b,1) = 0 Log(b,b) = 1
What are two properties of logarithms?
300
The range of f(x) is [-5,5] if the domain is [-5,5]
What is the range of f(x) = x if the domain is [-5,5]
300
The line of y = x
What is the line that a function is reflected over to find the inverse?
300
y = 2g(x) is a vertical stretch
What is the type of transformation applied if y = 2g(x)
300
10^3 = 1000
What is 1000 as a power of 10
300
log(81)/log(3)=4 if log(3,81) = 4
What is the change of base formula?
400
f(g(x)) = 3(-4x^6 - 5)^2 - 1 if f(x) = 3x^2 - 1 and g(x) = (-4x^6 - 5)?
What is f(g(x)) if f(x) = 3x^2 - 1 and g(x) = (-4x^6 - 5)?
400
f-1(x) = (x+7)/3
What is the inverse of f(x) = 3x - 7
400
f(x) = f(3x)+1
What is f(x) if you squeeze it horizontally by 3 the move it up 1
400
10^3.3034120705978 = 2011
What is 2011 written as a power of 10?
400
log(b,400) = 1.54 + 1.54
What is log(b,400) if log(b,20) = 1.54
500
The domain of f-1(x) is [0, infinity) because you limit the domain so f(x) has an inverse
What is Write the domain of f-1(x) if f(x) = x^2
500
f(g(h(x))) = (x^(x+2)^2) - 3
What is f(g(h(x))) if f(x) = (2^x) - 3, g(x) = x^2, and h(x) = x + 2
500
f(x) =3^x was: Reflected over x-axis stretched vertically by 2 shifted left 1 stretched horizontally by 3 shifted up 4
What are the transformations applied to f(x) = 3^x to get g(x) = -2*(3^(x+1)/3) + 4
500
7^3(x-2) = 7^5(3) x = 7
What is x if 21^x-2 = 35^3
500
log(9)=log(18)-log(2)=1.255-0.301=0.954
what is log(9) if log(18) = 1.255 and log(2) = 0.301
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