Let's analyze the functions in the image and address the question:

There are four functions displayed:

1. Function 1: A graph with a line crossing the y-axis.
2. Function 2: A table with points for the linear function.
3. Function 3: The equation $y = 4x + 3$.
4. Function 4: Described as having a slope of -5 and a y-intercept of 5.

Question:

• (a) Which function has the graph with a y-intercept closest to 0?

Solution:

We need to determine the y-intercept of each function.

1. Function 1 (Graph): From the graph, it seems the line crosses the y-axis around -1, making the y-intercept close to -1.
2. Function 2 (Table): To find the y-intercept, observe the table. When $x = 0$, $y = -4$. Thus, the y-intercept is -4.
3. Function 3 (Equation $y = 4x + 3$): The y-intercept is the constant term, which is 3.
4. Function 4 (Given slope -5, y-intercept 5): The y-intercept is explicitly given as 5.

Conclusion:

• Function 1 has the y-intercept closest to 0, since its y-intercept is around -1.

Let me know if you want further clarification!

Related Questions:

1. How do you calculate the slope from a graph or table of points?
2. What is the general formula for a linear equation, and how do you identify the slope and y-intercept?
3. How would you graph a function like $y = -5x + 5$ based on its slope and y-intercept?
4. Can a linear function have more than one y-intercept? Why or why not?
5. What is the significance of the slope in a real-world context, such as speed or rates?

Tip:

To quickly find the y-intercept from a table, look for the value of $y$ when $x = 0$.