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Domain, Range, Composition
Inverses
Transformations
Exponents
Logarithms
100
The sets of possible values for the input and the output, respectively.
What are domain and range?
100
This means that the equation is inverse.
What does f^-1(x) mean?
100
The proper term for these two changes is a dilation.
What is the proper term for a stretch or a squeeze?
100
An exponent means that the number is being multiplied by itself for 'x' amount of times. Ex. 5^x
What does an exponent mean?
100
It is either 10 or 'e,' which means 2.718.
What is the common base?
200
Two equations you could draw from either of these composite functions would be f(x)=2^x and g(x)=x+3.
What are two equations you could draw from these two composite functions, f(g(x))=(2^x)+3 and g(f(x))=2^(x+3)?
200
It is reflected over the line x=y.
What happens to the graph of a function when it is inverted?
200
It would be shifted to either the left or right by three.
What would happen to the graph of a function if this happened: -3+f(x) or 3+f(x).
200
125+1728=1853 (Hint, both are exponents involve the number 3).
What does 5^3+12^3 equal?
200
5 (Hint, base 5)
What is log(5,125)
300
A system which uses parenthesis and brackets to signify a number being either infinite (Ex. 4.999r) or finite (Ex. 5). No using notes.
What is interval notation?
300
The inverse of that equation would be f^-1(x)= square root of x+3.
What is the inverse of f(x)=x^2-3
300
This equation would be shifted to the right by 5 points, shifted up by 2, and flipped vertically over the y-axis.
What would happen if you were to subtract 5 from the 'x' value, add 2 to the entire equation, and make 'x' negative.
300
This exponential rule is equal to a^mn.
What exponential rule is (a^m)^n equal to?
300
log(a*b)
What is log(a)+log(b) equal to?
400
These three equations could be combined to form f(g(h(x)))=2^(3x+4)-3
What is one equation that f(x)=3x+1, g(x)=2^x-3, and h(x)=x+3 could be combined to form? Order is f(g(h(x))).
400
Inverse of f(x)=- square root of (5x-2)
What is f^-1(x)=1/5(x²+2)
400
Quadratic function moved down 2, right 5, and flipped over the x-axis.
What is f(x)=((x-5)^2)-2?
400
This is the justification of a^m*a^n=a^m+n.
Because there are 'm' groups of (a*a...*a) multiplied by 'n' groups of (a*a...*a), there are 'm'+'n' groups of (a*a*a*a...*a).
400
Evaluate without a calculator log(37,6) – log(9,81).
What is -8.8333?
500
The composite of those two functions would be g(h(x))=(2x-1)^2+3. R:[3, infinity) D: (-infinity, infinity)
What would be the composite of g(x)=x^2+3 and h(x)=2x-1, in the order g(h(x))? What would be the domain and range?
500
The noninverse equation of f^-1(x)=the cubed root of x+7.
What is What is f(x)=(x^3)+7?
500
The equation of an absolute value function moved up 3, right 4, and enlarged by 4.
What is f(x)=(|-x-4|+5)/4?
500
Simplify (a^5*a^61)+((a^3)/(a^-1))+((ab)^3) without using notes.
What is a^73+b^3?
500
The first four digits are 2.718 - what number is this and who invented the number?
What is 'e,' which was found by Euler.