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The question provided asks about a linear function \( f(x) = 5 - \frac{1}{2}x \), and it requires three parts to be solved:

### (a) Evaluate \( f(-2) \) and \( f(0) \):
We substitute the values of \( x \) into the function \( f(x) \).

For \( f(-2) \):
\[
f(-2) = 5 - \frac{1}{2}(-2) = 5 + 1 = 6
\]

For \( f(0) \):
\[
f(0) = 5 - \frac{1}{2}(0) = 5
\]

### (b) Find the zero of \( f(x) \):
To find the zero of the function, set \( f(x) = 0 \) and solve for \( x \):
\[
0 = 5 - \frac{1}{2}x
\]
\[
\frac{1}{2}x = 5
\]
\[
x = 10
\]

Thus, the zero of the function is \( x = 10 \).

### (c) Graph \( f(x) \):
The graph of a linear function like this one is a straight line. To graph \( f(x) \), use two points:
1. When \( x = 0 \), \( f(0) = 5 \) (the y-intercept).
2. When \( x = 10 \), \( f(10) = 0 \) (the x-intercept).

The slope of the line is \( -\frac{1}{2} \), meaning for every increase of 2 in \( x \), \( f(x) \) decreases by 1.

### How the graph can be used to determine the zero of \( f \):
The zero of \( f \) can be determined by finding the point where the graph intersects the x-axis. In this case, the zero is at \( x = 10 \), which is the x-intercept of the line.

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Would you like more details or further explanation on any part?

Here are five related questions:
1. How do you determine the slope from the equation of a linear function?
2. What is the significance of the x-intercept and y-intercept in a linear graph?
3. Can you find the equation of a line if you are given two points?
4. How does changing the slope affect the steepness of the line in a graph?
5. What is the general form of a linear function?

**Tip:** When graphing a linear function, always plot at least two points, such as the intercepts, to ensure accuracy.

For the linear function f(x) = 5 - (1/2)x: (a) evaluate f(-2) and f(0); (b) find the zero of f; and (c) graph f. How can the graph of f be used to determine the zero of f?

Learn how to evaluate the linear function f(x) = 5 - (1/2)x, find the zero of the function, and graph it. This problem involves key concepts like slope-intercept form and zeros of a function, suitable for students in Grades 8-10.

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