Question
Math Practice U6 L1
Link to U6 L1 - 9 Math Practice
Live Lesson Recording
*Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!
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?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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?
Link to U6 L1 - 9 Math Practice
Live Lesson Recording
*Passcode can be found on the Connexus Pushpin under your Math Class! Use the one for Mrs. Garcia!
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?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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?
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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!
### 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!
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