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Let's go through each question step-by-step using the information given for the four functions.

### Analysis of Each Function:
1. **Function 1**: The graph shows a line with a negative slope. We can observe that the slope appears to be less steep than Function 3 (which has a slope of -5).
2. **Function 2**: Given as a table of points. We can calculate the slope by finding the difference in \( y \)-values over the difference in \( x \)-values. For example:
   \[
   \text{slope} = \frac{-8 - (-12)}{-1 - (-2)} = \frac{4}{1} = 4
   \]
   So, the slope of Function 2 is 4.
3. **Function 3**: Defined by the equation \( y = -5x - 2 \), where the slope is -5, which is steep and negative.
4. **Function 4**: Defined with a slope of 2 and a \( y \)-intercept of 3.

### Solving Each Part:

**(a) Which function’s graph is the steepest?**

- **Answer**: The steepest slope in terms of magnitude is -5 in Function 3. Thus, **Function 3** is the steepest.

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**(b) Which functions have graphs with \( y \)-intercepts greater than \(-3\)?**

- Function 1: Observing the graph, the \( y \)-intercept appears to be at -2.
- Function 2: From the table, when \( x = 0 \), \( y = -4 \), which is less than -3.
- Function 3: The equation \( y = -5x - 2 \) has a \( y \)-intercept of -2.
- Function 4: The \( y \)-intercept is 3.

- **Answer**: **Function 1, Function 3, and Function 4** have \( y \)-intercepts greater than -3.

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**(c) Which function has the graph with a \( y \)-intercept farthest from 0?**

- \( y \)-intercepts:
  - Function 1: -2
  - Function 2: -4
  - Function 3: -2
  - Function 4: 3

The \( y \)-intercept farthest from 0 in absolute value is -4 from **Function 2**.

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### Final Answers:

- **(a)**: Function 3
- **(b)**: Functions 1, 3, and 4
- **(c)**: Function 2

Would you like more details on any of these calculations?

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Here are some related questions to further your understanding:
1. How do we find the slope between two points on a line?
2. What does the steepness of a line signify in real-world terms?
3. How do we determine a line's intercept from its graph?
4. Why is the absolute value important in determining the farthest distance from 0?
5. What are the characteristics of a line with a positive slope versus a negative slope?

**Tip**: To identify the steepest graph, always compare the absolute values of the slopes. The higher the absolute value, the steeper the line.

Four different linear functions are represented. Answer questions based on the graph, table, and equations given for the functions.

Explore how to determine the steepness of a graph, identify y-intercepts greater than a certain value, and find the y-intercept farthest from zero for four different linear functions represented by graphs, tables, and equations.

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