Math Practice U6 L1

Question

Link to U6 L1 - 9 Math Practice
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Function of the Day:
A mailman is delivering packages to a small neighborhood. The arrows in each diagram show where the packages would be delivered.

What do you know?

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Vocabulary Terms - Define/Illustrate

Input
Output
Function

5 Problems - SHOW ALL WORK!

How can we determine from a graph if a function is shown or not?

How can you tell from a table of values if the relationship is a function or not?

How can you tell from an equation if the relationship is a function?

Is the number of students on a field trip a function of the number of buses used? Explain.
Is the time it takes you to run a 100-meter race a function of the speed you run? Explain.


What do I need help with?

Answer 1

It looks like you're working on a math assignment involving functions! Let's break down each section step by step.

What do you know?

You can list specific observations or facts that relate to functions. Here are some ideas you might want to consider:

1. A function relates an input to exactly one output.
2. The vertical line test can be used to determine if a graph represents a function.
3. In a table of values, each input (or x-value) must correspond to one output (or y-value) for the relationship to be a function.
4. An equation can be checked for function status by ensuring that every x-value leads to only one corresponding y-value when solved for y.
5. Functions can be linear or nonlinear based on how their graph appears.
6. The domain of a function is the set of all possible input values.
7. The range of a function is the set of all possible output values.
8. Some relationships may appear to be functions in restricted domains but may not be functions in a larger context.
9. Functions can be expressed using tables, graphs, or equations.
10. Real-world situations can often be modeled as functions.

Vocabulary Terms - Define/Illustrate

1. Input: The value you substitute into a function. Example: In the function \( f(x) = x + 2 \), if \( x = 3 \), the input is 3.

2. Output: The result you get after applying the function to the input. Example: For \( f(3) = 3 + 2 = 5 \), the output is 5.

3. Function: A relationship where every input is associated with exactly one output. Example: The function \( f(x) = x^2 \) takes any real number input and produces one unique output (the square of that number).

5 Problems - SHOW ALL WORK!

1. Determining if a function is shown on a graph:

   • Use the vertical line test: If a vertical line crosses the graph at more than one point, it is not a function.
   • Example: The graph of a circle fails this test since a vertical line can intersect it twice.

2. Determining from a table of values:

   • Check if any input (x-value) appears more than once in the table. If it does, it is not a function.
   • Example: | x | y | |---|---| | 1 | 2 | | 2 | 3 | | 1 | 4 | (fails, since x = 1 has two different y-values)

3. Determining from an equation:

   • Solve for y; if for a given x, there is only one y that can be obtained, it is a function.
   • Example: The equation \( y = x^2 \) is a function because for each x, there is one specific y.

4. Is the number of students on a field trip a function of the number of buses used?

   • Yes, this is a function if we assume a specific capacity for the buses. Each number of buses will correspond to a possible number of students, but the relationship may depend on the maximum capacity.

5. Is the time it takes you to run a 100-meter race a function of the speed you run?

   • Yes, this is a function. If your speed is maintained, then there will always be a consistent time taken for the race based on the relationship \( time = \frac{distance}{speed} \).

What do I need help with?

If you have specific questions or need help on certain problems, let me know so I can assist you further!