1. **State the problem:** We are given the function $y = 4x - 2$ and asked to describe its domain and range, and compare its graph to the graph of $y = 4x$. 2. **Domain and range of linear functions:** For any linear function of the form $y = mx + b$, the domain is all real numbers because $x$ can take any value. 3. **Domain of $y = 4x - 2$:** Since there are no restrictions on $x$, the domain is: $$\text{Domain} = (-\infty, \infty)$$ 4. **Range of $y = 4x - 2$:** Because the function is linear with slope $4 \neq 0$, the output $y$ can also take any real value. Thus, $$\text{Range} = (-\infty, \infty)$$ 5. **Compare $y = 4x - 2$ to $y = 4x$:** The graph of $y = 4x - 2$ is the graph of $y = 4x$ shifted downward by 2 units. 6. **Explanation:** The slope $4$ is the same in both functions, so the steepness and direction of the line are identical. The $-2$ subtracts 2 from every $y$ value, moving the entire line down. 7. **Summary:** - Domain: $(-\infty, \infty)$ - Range: $(-\infty, \infty)$ - Graph of $y = 4x - 2$ is the graph of $y = 4x$ shifted down by 2 units.