Functions: Domain, Range, Composition
Functions: Inverses
Functions: Transformations
Exponents
Logarithms
100
(-8,5] Is the correct way of writing the domain.
What is the correct way of writing the domain of a function f(x), from 5 to 8, if 5 is inclusive but -8 isn't?
100
If input x into the function produces output y, then y into the inverse function produces output x.
What is the condition a function needs to have in order to have an inverse?
100
f(x)=x^2+3 is the transformed function
If f(x)=x^2 is vertically translated by 3 units, how would the transformed function will look like?
100
(a^m)^n= (a*a*...a)-m times-^n (a*a*..a)-m times-(a*a*..a)-m times-(a*a*...a)-m times- All of it n times=(a^m)^n
Justify the rule: (a^m)^n
100
Base and argument
What are the parts of a logarithm?
200
f(g(9))=13
What is f(g(9)) if f(x)=x^2+4 and g(x)=x/3?
200
The horizontal line test
What method can we use to prove a function is not one to one?
200
They affect the domain.
What do horizontal transformations affect?
200
It equals to 3^(-4) * 4^3
Simplify 3^4 * 3^(-8) * 4^3
200
It equals log(a*b)
Complete the property: Log(a)+log(b)=
300
Domain is all possible x values while range are the y ones.
What is the difference between domain and range?
300
It is not because for every input there is more than one output.
Given the following table of values, explain why it is not a one-to-one function. x -3 -2 0 2 3 --------------- y 7 2 -2 2 7
300
A vertical shift down of 5
Explain what transformations are done to the following function: Original function: f(x)=3^x Transformed function: f(x)=3^x-5
300
(2^2)^2x-1=(2^3)^x+1 x=5
Solve x: 4^2x-1=8^x+1
300
2^3=8 is the exponential form.
Rewrite the following logarithm as an exponential form: Log2(8)=3
400
F(x)=x^2+3 G(x)=x-1 There is more than one solution
What is f(x) and g(x) if f(g(h))=(x-1)^2+3
400
f^-1(x)=3x-8
What is the inverse function of f(x)=(x+8)/3
400
A squeeze, if c>1 A stretch if <0c<1 A flip over the y axis if c<0
Given f(c*x), a horizontal dilation, list the three transformations that can be done to a function depending on the c value.
400
Growht: Population Decay: Carbon 14 throughout the years
Give an example of exponential growth and another one for decay.
400
Log3(3)+log3(10) or log3(5)+log3(6) or Log3(π)+log3(30/π)
Write at least three different possibilities by which you can get log3(30)
500
D=(-∞,∞) R=(-∞, 1]
What is domain and range of f(x)=-(x-1)^2+1
500
We need to restrict the values, only accepting those that are 0 or greater. y=√x (Principal Square root, always positive).
What can we do to y=x^2 to make it one-to-one?
500
It will look like this: g(x)=-(1/2(x+3))^2-3)
After doing the following transformations to the function f(x)=(x-1)^2-1, how will the function look like? Transformations: f(x) was shifted 4 units to the left, 2 units down, flipped vertically, stretched horizontally by a factor of 2
500
(3*3*2)^10=(2*2)^5 (3^x) So:3^10*3^10*2^10=2^5*2^5*3^x So:3^20=3^x x=20
If 18^10=(4^5)(3^x), what is x?
500
Log2(32) = Log2 (2^5) So: 5Log2(2)=5
Use an example to explain why Log2(32) equals 5.
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