Question

HELPP!!!!!!!!!!!
Match the word with the definition. You CAN use your Notes!

Question 1 options:

Practical Range


Domain


Function Notation


Vertical Line Test


Range


Practical Domain


Relation


Function

1.
A mapping from a set of inputs to a set of outputs
2.
Set of allowable inputs (usually x-values)
3.
Set of allowable outputs (usually y-values)

4.
A relation in which every element of the domain is assigned to exactly one element of the range
5.
If two points of a graph lie on ANY vertical line, the graph is NOT a function

6.
A function equation written so that the output variable (y) is replaced with the function’s name and the input variable
7.
The set of REALISTIC inputs

8.
The set of REALISTIC outputs

Answer 1

Answers:

1. Relation
2. Domain
3. Range
4. Function
5. Vertical Line Test
6. Function Notation
7. Practical Domain
8. Practical Range

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Explanation:

1. A relation is basically anything where we connect one variable to another. Usually there are math operations involved to have a predictable rule. For example, y = x+5 says "add 5 to the x input to get the y output". But we won't always have a rule like this to connect x and y.
2. The domain is the set of allowed inputs (x values). For example, if we had the function y = 1/x, then we can plug in anything but x = 0. This is to avoid a division by zero error.
3. The range is the set of allowed output y values. You can use a graph to determine the range, or find the domain of the inverse (assuming one exists).
4. This is basically saying each input goes to exactly one output only. If such a thing happens, then the relation is a function.
5. A visual way to test if you have a function is to use the vertical line test. If you can pass a vertical line through more than one point, then it is said to have failed the vertical line test and we don't have a function. Failing the vertical line test shows that a particular x value leads to multiple y outputs.
6. Function notation is when we replace y with something like f(x) so the function name is a bit more descriptive.
7. Let's say we had the function f(x) = 100/x. The x represents the number of people, and f(x) is the average cost per person. Before I mentioned that the domain is anything but 0, to avoid a division by zero error. Realistically, we also would make x the set of positive whole numbers (1,2,3,4,...) since x is the number of people. This is one example where a theoretical domain shrinks down to a more practical one.
8. Since the domain shrinks in problem 7, the range is likely to shrink as well. Use a graph or table to see why this happens.