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.

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.