Functions: Domain, Range, Composition
Functions: Inverses
Functions: Transformations
Exponents
Logarithms
100
all real numbers for domain, all real numbers greater than 0 for range
What is domain and range of an absolute value parent function or quadratic parent function?
100
-y=x
What is the inverse of y=x?
100
parabola function shifted up 1
What is x^2 +1?
100
x*4=32 x=8
What is 2^4x=2^32?
100
logs are exponents so (log2)^3 will be log(8)
Why is log(8) three times log(2)?
200
domain is all real numbers, range is all real numbers greater than or equal to -7
What is what is the domain and range of a quadratic function or absolute value function shifted left 53 and down 7?
200
-x^2
What is the inverse of a quadratic?
200
Square root function shifted left 7
What is square root of x+7?
200
15=4x-1 x=4
What is 5^15=5^4x-1?
200
2 because 10^2 is 100
What is log base10 of 100?
300
domain is all real numbers greater than -3 range is all real numbers greater than 0
What is the domain and range of a square root function shifted left 3?
300
negative square root of x
What is the inverse of a square root function?
300
quadratic function shifted left 2, up 1
What is x^(2+2)+1?
300
a^-1*a^1 must equal a^0 which is 1. Therefore a^-1 must equal 1/a because a*1/a=1
What is a^-1=1/a?
300
4 because 10^4 is 10000
What is log(10000)?
400
domain is all real numbers, range is all real numbers greater than or equal to 36213612.
What is the domain and range of an absolute value function or quadratic stretched horizontally by 4, stretched vertically by 3, moved up 36213612?
400
absolute value of (1/2x)-2 2,-1 becomes -1,2 -2,-1 becomes -2,-1 4,0 becomes 0,4 -4,0 becomes 0,-4
What is the inverse of a absolute value function shifted down 2 and stretched horizontally by 2?
400
quadratic function shifted right 6, down 4, and flipped over the x-axis
What is -x^(2-6)-4?
400
(2^2)^3x-1=(2^3)^x+1 2^6x-2=2^3x+3 6x-2=3x+3 3x=5 x=5/3
What is 4^3x-1=8^x+1?
400
log baseb(x)=log basek(x)/log basek(b)
What is the change of base formula?
500
domain is all real numbers greater than or equal to 4 range is all real numbers greater than or equal to 0.
What is the domain and range of a square root function shifted right 4, stretched vertically by 3?
500
x^(2*3)+2 1,3 becomes 3,1 2,12 becomes 12,2 -1,3 becomes 3,-1
What is the inverse of a quadratic function stretched vertically by 3 and shifted up 2?
500
square root function flipped over the x axis, flipped over the y-axis, shrunken vertically by 1/5, stretched horizontally by 2, up 8, right 6.
What is -1/2 square root of (-1/5x+6)+8?
500
8^195 (8^3-8^2-8+1)=441(2^x) 8^195 (512-64-8+1)=441(2^x) 8^195 (441)=441(2^x) 8^195=2^x x=585
What is 8^198-8^197-8^196+8^195=441(2^x)?
500
log baseb(x)=log basek(x)/log basek(b) log base5(100)=log base10(100)/log base10(5) 2.86
What is log base5(100) rounded to the nearest hundredth?
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