1. **State the problem:** We are given the function $g(x) = 2x - \frac{1}{2}$ and want to understand or analyze it. 2. **Formula and rules:** This is a linear function of the form $g(x) = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $m = 2$ and $b = -\frac{1}{2}$. 4. **Interpretation:** The slope $2$ means for every increase of 1 in $x$, $g(x)$ increases by 2. 5. **Find intercepts:** - To find the y-intercept, set $x=0$: $$g(0) = 2 \times 0 - \frac{1}{2} = -\frac{1}{2}$$ - To find the x-intercept, set $g(x) = 0$: $$0 = 2x - \frac{1}{2}$$ $$\Rightarrow 2x = \frac{1}{2}$$ $$\Rightarrow x = \frac{\cancel{2} \times x}{\cancel{2}} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$$ 6. **Final answer:** The function $g(x) = 2x - \frac{1}{2}$ has slope 2, y-intercept $-\frac{1}{2}$, and x-intercept $\frac{1}{4}$.