The two functions, $f(x) = x$ and $g(x) = x - 3$, are linear functions. They have the same slope but different y-intercepts.

The relationship between these functions can be described as follows:

• $g(x)$ is a vertical translation of $f(x)$ downward by 3 units. This means that every point on $f(x)$ is shifted 3 units downward to obtain $g(x)$.

Mathematically, $g(x)$ can be rewritten as $f(x) - 3$, showing that $g(x)$ is the same as $f(x)$ but with all the y-values decreased by 3.

Would you like more details or have any questions? Here are five related questions to deepen understanding:

1. What is the slope of both functions $f(x)$ and $g(x)$?
2. How would you graph both functions on the same coordinate plane?
3. What would happen if the transformation applied was $g(x) = x + 3$ instead of $g(x) = x - 3$?
4. How would you describe the relationship between $f(x)$ and $g(x)$ if the transformation was $g(x) = 2x - 3$?
5. Can you describe how the equation $g(x) = x - 3$ affects the intercepts on the graph?

Tip: When comparing two linear functions, pay close attention to the changes in their slopes and y-intercepts to understand the type of transformation.