Functions: Domain, Range, Composition
Functions: Inverses
Functions: Transformations
Exponents
Logarithms
100
Domain: [0,∞) Range: [0,∞)
What is the domain and range of the square root function?
100
How to test if a function is one to one.
What is the horizontal line test?
100
y= ((x/4)^2)+2
What is the equation for a quadratic function shifted up 2 and stretched horizontally by 4?
100
(a*a*a...a(n times)) * (a*a*a...a(m times))= a*a*a...a (n+m times)= a^m+n
Justify the rule: a^m +a^n= a^m+n
100
log(b,x)=y b= base x= argument
What do the b and x stand for in the logarithm?
200
f(g(x))= (x/3)^2 if f(x)=x^2 and g(x)=x/3
What is an example of composition?
200
Swap x and y's places in the function and simplify to isolate y.
What is a way to find the inverse of a function?
200
It flips the function over the y or x-axis.
What is the role of a negative sign in a function?
200
√5=5^(1/2)
What is another way to write √5 (square root)?
200
(log(b,0)=1) = (b^0=1)
Justify the property: log(b,0)=1
300
Domain: x≠0 Range: x≠0
What is the domain and range of a inverse/ reciprocal function?
300
The inverse is y=((x+4)/2)^1/3
What is the inverse of y=2(x^3)-4
300
y= -(5x+2)^3
What is the equation of a cubic function flipped over the x-axis, shrunk horizontally, and shifted left 2?
300
(a*a*a...a(n times))/(a*a*a...a(m times)=a^n-m (amount of m in n is canceled out)
Justify (a^n)/(a^m)=a^n-m
300
(log(x,x)=1) = (x^1=x)
Justify the property: log(x,x)=1
400
Domain: (-∞,∞) Range: (-∞, 3] Absolute value function
What is the domain, range, and parent function of f(x)= -|2x|+3
400
f^-1(x)
What is the notation of inverse.
400
y= -4^(6x-5) +2
What is the equation of a exponential function flipped over the x-axis, stretched vertically by 2, shrunk horizontally by 6, shifted right 5 and up 2.
400
x^(-2)=1/x^2
What do you do if there is a negative exponent?
400
=log(ab)
Simplify log(a) + log(b)
500
f(f(g(x)))= 2(2(x^3)+4)+4
What is f(f(g(x))) if f(x)=2x+4 and g(x)=x^3
500
x=y
When does the original and inverse function cross?
500
y= -2((1-x^2)/4)^(1/2) -3
What is the equation of a half circle function flipped over the x-axis, stretched vertically by 2 and horizontally by 4, and shifted down 3
500
(a^1/n)*(a^1/n)... (a^1/n) (n times)=a n√a*a...a (n times)=a
Justify a^(1/n)= n√a
500
y=log(10x) is y=log(x)+1
Compare the graph of y = log (x) and the graph of y = log (10x). How are they related.
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