- Domain: set of values that can imputed into the functions
- Range: the set of values the functions produces
What are the definitions for domain and range?
100
- The horizontal line test.
What test does a function have to be able to pass to be “one-to-one”?
100
- Shifted right 2 and up 3 from the original equation f(x)= x^2
Graph the equation f(x) = (x-2)^2 +3 and f(x) =x^2 as the original equation. How is the equation transformed?
100
5^32 (simplified through multiplication)
Simplify 5^x * 5^y
x+y= 32
100
Log?(x)=y
-base
Log?(x)=y
What does the question mark represent?
200
-For every input there is only one output.
-Function: a straight horizontal line
Not a Function: a circle
What is the main rule of a function? Give an example of a function and something that is not a function.
200
x x^2
1 2
2 4
3 9
x √x
2 1
4 2
9 3
You can conclude that these tables are inverses of each other.
What do you can you conclude from both these tables.
200
- If b is “+b” than it is shifted left but if its “-b” than it is shifted right
- If c is “+c” than it is shifted up but if its “-c” than it is shifted down
Give the general rules of transformations using the equation f(x) = (x+b) +c.
200
12^3 (simplified through division)
Simplify 12^x/ 12^y
x-y= 3
200
Log x(??)=y
-argument
What does the question mark represent?
300
x (independent) y (dependent)
1 1
2 2
3 3
3 4
4 5
2 6
1 7
You can conclude that this is not a function because there are several outputs that are the same.
What can you conclude from this table? Explain why:
300
- No it is not possible for this parent function, because it’s “inverse” wouldn’t be a function because it wouldn’t pass the vertical line test.
Is it possible for the parent function f(x)= x^2 to have an inverse? Explain your reasoning.
300
- Given f(x) and “c” is a constant
- c*f(x) and c>1 it is vertically stretched but if 01 it is horizontally shrunk but if 0
Give the general rules of dilation
300
- (a*a*a*…) --> m
- (a*a*a…)(a*a*a…)(a*a*a…)(…) --> n
- a^mn --> power of the power
Justify (a^m)^n= a^m*n
300
It finds the exponent that you have to raise a base number to, in order to get the argument.
What is the point of a Logarithm?
400
- Domain: All Real Numbers
- Range: [-3,infinity)
- Parent Function: quadratic
State the domain, range, and the of this function: y= 2(x-5)^(2)-3
400
Inverse is: g(x)=(1/2)x-3
What is the inverse of the equation f(x)= 2x+3
400
- Cubic; vertically stretched by 2; up 45; right 5 from the function f(x)= x^3
Graph the equation f(x)= 2(x-5)^3 +45. How it is transformed from the parent function?