Questions: Translate each graph as specified below. (a) The graph of y=f(x) is shown. Translate it to get the graph of y=f(x)-3. (b) The graph of y=g(x) is shown. Translate it to get the graph of y=g(x+4).

Solution Steps

The graph of $y = f(x)$ needs to be translated to get the graph of $y = f(x) - 3$. The transformation is a vertical shift down by 3 units. This is because subtracting 3 from the function $f(x)$ affects the y-coordinate of each point.

To obtain the graph of $y = f(x) - 3$, take every point $(x, y)$ on the graph of $y = f(x)$ and shift it down 3 units to $(x, y-3)$. For example, the endpoint at $(1, 0)$ on the original graph should be moved to $(1, -3)$.

The graph of $y = g(x)$ needs to be translated to obtain $y = g(x+4)$. The transformation is a horizontal shift to the left by 4 units. This is because adding 4 to the input $x$ before applying the function $g$ affects the x-coordinate of each point.

To get the graph of $y = g(x+4)$, take each point $(x, y)$ on the original graph of $y = g(x)$ and shift it 4 units to the left, resulting in the point $(x-4, y)$. For example, the vertex at $(0, 0)$ should shift to $(-4, 0)$.

Final Answer: