The function provided in the image is $f(x) = \frac{1}{2}x - 7$.

This is a linear function in the form $f(x) = mx + b$, where:

• $m = \frac{1}{2}$ is the slope of the line,
• $b = -7$ is the y-intercept, which is the point where the line crosses the y-axis.

Key Properties of the Function:

1. Slope ($m$): The slope is $\frac{1}{2}$, meaning for every 1 unit increase in $x$, $f(x)$ increases by $\frac{1}{2}$ units.
2. Y-intercept ($b$): The y-intercept is -7, so the line crosses the y-axis at the point (0, -7).
3. X-intercept: To find the x-intercept, set $f(x) = 0$ and solve for $x$: $0 = \frac{1}{2}x - 7$ $\frac{1}{2}x = 7$ $x = 14$ So, the line crosses the x-axis at the point (14, 0).

Would you like more details on any specific aspect or have any questions?

Related Questions:

1. How would you graph the function $f(x) = \frac{1}{2}x - 7$ on the coordinate plane?
2. What is the meaning of the slope and y-intercept in a real-world context?
3. How does changing the slope $\frac{1}{2}$ affect the graph of the function?
4. How would you find the point of intersection between this line and another line, say $g(x) = -x + 3$?
5. What is the range of the function $f(x) = \frac{1}{2}x - 7$?

Tip:

When graphing a linear equation, it's helpful to identify the y-intercept and another point on the line (like the x-intercept) to draw the line accurately.