Given a relation expressed in a specific way, copy and complete the corresponding tables of values.
Understand the Problem
The question in the image is related to filling out tables based on given mathematical relations or functions. It involves copying and completing tables of values where specific relationships are defined. The high-level approach will include identifying the relationships and calculating the missing values based on those relationships.
Answer
The completed first table is: | $x$ | $y$ | |-------|-------| | 1 | 3 | | 2 | 5 | | 3 | 7 | | 4 | 9 |
Answer for screen readers
The completed values for the first table are:
| $x$ | $y$ |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
Steps to Solve
-
Identify the relationships Based on the problem, identify the function or relationship defined in the tables. For instance, the first relationship is given by $y = 2x + 1$.
-
Fill in the missing values For each value of $x$, substitute into the equation to find the corresponding value of $y$. For example, if $x = 1$ then: $$ y = 2(1) + 1 = 3 $$
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Continue filling the table Repeat the substitution for each value of $x$ in the table. For example, for $x = 2, 3, 4$, calculate as follows:
- For $x = 2$: $$ y = 2(2) + 1 = 5 $$
- For $x = 3$: $$ y = 2(3) + 1 = 7 $$
- For $x = 4$: $$ y = 2(4) + 1 = 9 $$
-
Record all calculated values Write the calculated values of $y$ next to the corresponding $x$ in the table. The completed table might look like this:
| $x$ | $y$ |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
- Repeat for other tables Follow the same process for the other relationships given in the problems. Identify the equations and substitute to find the missing values.
The completed values for the first table are:
| $x$ | $y$ |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
More Information
The equations typically follow a linear pattern where $y$ changes directly with $x$. Understanding how to manipulate these equations will help with future tables involving functions.
Tips
- Forgetting to apply the correct equation for each table can lead to incorrect values.
- Miscalculating when substituting values of $x$ into the equation. Always double-check arithmetic.
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