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(b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x)+4.

To translate the graph of \( y = g(x) \) to obtain the graph of \( y = g(x) + 4 \), you need to shift the entire graph upward by 4 units. This means that for every point \((x, y)\) on the original graph, the corresponding point on the translated graph will be \((x, y + 4)\).

Here is a step-by-step process for translating the graph:

1. Identify key points on the original graph. For example, points where the curve crosses the x-axis and y-axis.
2. Add 4 to the y-coordinate of each of these points to obtain the new coordinates.
3. Plot these new points on the graph.
4. Draw the new curve passing through these new points, maintaining the same shape as the original graph.

Let’s illustrate this process with a few points from the given graph:

1. The point where the graph crosses the x-axis: approximately \((1.5, 0)\). The new point will be \((1.5, 4)\).
2. The point where the graph crosses the y-axis: approximately \((0, 2)\). The new point will be \((0, 6)\).

You will shift all other points similarly and redraw the graph with the new points.

Would you like more detailed steps or assistance with any specific part of this translation? Here are some follow-up questions you might consider:

1. Do you need help with identifying specific points on the graph for translation?
2. Would you like a more detailed explanation of the translation process?
3. Do you need assistance with another type of graph transformation?
4. Are there any other parts of the problem you need help with?
5. Would you like to see an example of translating a different function?

**Tip:** When translating a graph vertically by adding or subtracting a constant, only the y-coordinates of the points change, while the x-coordinates remain the same.

Learn how to translate the graph of y=g(x) to y=g(x)+4. Understand the process of shifting a graph vertically by 4 units with detailed steps and examples. Suitable for high school students studying graph transformations.

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