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Looking at the graph provided, we have a straight line representing the function \( y = f(x) \), and we are asked to find the values of \( f(x) \) for specific values of \( x \) (1, 2, 3, and 4.5).

To determine these values, we can read the corresponding points from the graph where the line intersects at these \( x \)-coordinates:

1. For \( x = 1 \), follow the vertical line from \( x = 1 \) on the \( x \)-axis to the graph of the function. It seems to intersect the line at \( y = 0 \). Therefore, \( f(1) = 0 \).
2. For \( x = 2 \), the line intersects the function at approximately \( y = 1 \). Thus, \( f(2) = 1 \).
3. For \( x = 3 \), the line intersects at \( y = 2 \). Thus, \( f(3) = 2 \).
4. For \( x = 4.5 \), follow the vertical line up from \( x = 4.5 \), and it seems to intersect at around \( y = 3.5 \). Therefore, \( f(4.5) = 3.5 \).

In summary:
- \( f(1) = 0 \)
- \( f(2) = 1 \)
- \( f(3) = 2 \)
- \( f(4.5) = 3.5 \)

Would you like further details or have any questions? Here are some related questions to think about:

1. What is the slope of the line \( y = f(x) \)?
2. Can you find the equation of the line based on the points and slope?
3. How would you find \( f(x) \) for \( x = 5 \) based on this line?
4. How do you interpret the function graphically in terms of its rate of change?
5. What would the function's behavior look like for negative values of \( x \)?

**Tip:** For a linear function, once you know the slope and one point, you can easily write the equation for the line.

Based on the given line graph, determine the values of the function f(x) at x-values 1, 2, 3, and 4.5.

Explore how to read function values directly from a line graph. This guide provides a step-by-step approach to finding f(x) at x-values 1, 2, 3, and 4.5, illustrated with a linear function y = mx + c. Suitable for students in Grades 8-10.

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