The problem states that the graph of $g(x)$ is the graph of the parent function $f(x) = x$ translated 3 units upward. To find the y-intercept of $g(x)$, let’s break it down step-by-step.

Step 1: Parent Function

The parent function $f(x) = x$ is a straight line passing through the origin (0, 0). So the y-intercept of the parent function $f(x)$ is 0.

Step 2: Translation Upward

When the graph is translated 3 units upward, the equation of the new function becomes: $g(x) = f(x) + 3 = x + 3$ This means every point on the graph of $f(x) = x$ is shifted 3 units up.

Step 3: Finding the y-Intercept

To find the y-intercept of $g(x)$, we set $x = 0$: $g(0) = 0 + 3 = 3$ Thus, the y-intercept of $g(x)$ is 3.

Final Answer:

The y-intercept of the function $g(x)$ is 3.

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

1. What happens to the y-intercept if the translation is downward by 4 units?
2. How do translations affect the slope of a linear function?
3. If $g(x) = x - 2$, what is the new y-intercept?
4. What is the equation for a function translated 5 units to the left?
5. How would a vertical stretch by a factor of 2 affect the graph of $f(x) = x$?

Tip: Whenever a function is translated upward or downward, the only thing that changes is the y-intercept, while the slope remains the same.