Chapter Sections 4.1-4.4 Flashcards
How do you know if a function is a one to one function?
If a horizontal line intersects the graph once
When stating domain of things such as f(g(x)) what should you keep in mind?
Find the domain of the inner part. In this example it would be the domain of g(x) and then add it on to the final domain of f(g(x)) this would be the whole domain unless it is all real numbers or if it is inequalities then they might not be included
what happens with domain and range of f(x)
The domain of f(x) becomes the range of f(x)^-1 and the range of f(x) becomes the domain of f(x)^-1 and switch points on graph so a point (1,2) on graph f(x) is actually (2,1) on graph f(x)^-1
How do you find the inverse?
Switch y and x in the equation
How do you find the a unit in a list of numbers?
You find the ratio of consecutive outputs (or y) if it is constantly the same number then that is a if not then it is not a exponential function
To switch a graph f(x)=a^x over the y axis what do you do?
It would be -f(x)=a^x
To switch a graph f(x)=a^x over the x axis what do you do?
It would be f(x)= -a^x
In logarithms can a be equal to one?
No! It can’t be equal to one and has to be bigger than 0
To find domain of logarithms what do you do? Ex f(x)=log(2-x)
You put it as 2-x>0 and find x
Find domain of ln(x+1)/(x)
(X+1)/(x)>0 then you get the asymptotes which are 0 and -1 and test numbers before -1 in between 0 and -1 and then after 0. Whichever are positive are within the domain.
What is the base function for log equation
F(x)=logx
2
What if the base graph for log equations is flipped over x axis
F(x)=log x Or f(x)= -logx
1/2 2
To flip the base function of log equation over the y axis
F(x)= log -x
2
In y = log x
a
What are some restrictions
A>0
X>0
A cannot be equal to 1
When should you take out negative x answers
When you get answers for x in logarithms make sure if you need both positive or negative. X can’t be negative but if it is squared then negative is ok to use.
