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MATH1113
| Question | Answer |
|---|---|
| define a relation | set of ordered pairs |
| define a function | for every input there is only one output |
| difference between relations and functions | relations can have multiple outputs for every input, functions cannot |
| example of a relation | (cat, meow) U (dog, meow) U (cow, meow) |
| example of a function | (cat, meow) U (dog, bark) U (cow, moo) |
| does (1,3) (3,3) (2,7) represent a function | yes, for every input there is only one output |
| what is function notation | y = f(x) |
| what is interval notation | a range of numbers using parentheses and brackets |
| strategy for finding the domain of a function | find which x-values are not included, the domain is x-values included in a function |
| find the domain of square root x+4 over x+1 | [-4,-1) U (-1, infinity) |
| if a square root is in the denominator is it included | no therefore it will have paranthesis |
| define the range of a function | the y-values included in a function |
| identify the range of square root x-3 | [0, infinity) |
| is y=3 in the range of 2x/x-2 | yes the answer is 3 |
| define roc of a function | the average speed at which a function changes over a specific time |
| roc formula | f(b) - f(a) / b - a |
| what is the connection of roc with the slope of a line | roc = slope |
| is an average an exact number | no |
| explain the process of function composition | use the output of one function as the input for another function |
| how to check if an equation is a one to one on a graph | vertical line test |
| explain what it means for a function to be one-to-one | for every output there is only one input and vise versa, no x's or y's repeating |
| what does it mean for a function to have an inverse | to switch the inputs and outputs and still have a function, to do the reverse of a function but it still works as a function |
| why must a function be a one to one to have an inverse | you must be able to switch the input and output and still have a function which only can happen if the problem is a one to one |
| give a real world example of a one to one function | name --> SSN |
| when a function says function of x what is the input and what are you solving for | the input is x and you are solving for y |
| ex of an interval notation | [a,b} |
Created by:
lilyv5