The image shows a set of 3D surface plots, labeled A through F, representing the function $z = \sin(x) - \sin(y)$.

To match the correct graph to the function, let's analyze the given function mathematically:

1. Function Behavior: $z = \sin(x) - \sin(y)$ This represents the difference between two sine waves in the x and y directions, respectively.

2. Key Features:

   • The sine function oscillates between -1 and 1, so this function should also oscillate, with a maximum value of 2 (when $\sin(x) = 1$ and $\sin(y) = -1$) and a minimum value of -2 (when $\sin(x) = -1$ and $\sin(y) = 1$).
   • The surface will exhibit periodic waves in both the x and y directions, since sine is periodic.
   • The function should look symmetric, as the shapes created by $\sin(x)$ and $\sin(y)$ are mirror images due to their simple oscillatory nature.

Analysis of the Plots:

• Plot F seems to match the expected features of the function $z = \sin(x) - \sin(y)$. It shows a repeating wave pattern in both directions and an overall periodic structure, which aligns with how sine waves behave. The surface shows peaks and troughs as expected for the difference of sine functions.

Thus, the correct plot that represents the function $z = \sin(x) - \sin(y)$ is F.

Would you like more details about how the graph behaves or have any other questions?

Related Questions:

1. How do the oscillations of sine functions combine in different functions?
2. What are the maximum and minimum points of $z = \sin(x) - \sin(y)$?
3. How would the graph change if the function was $z = \sin(x) + \sin(y)$?
4. What is the period of this function along both the x and y axes?
5. How would shifting $x$ or $y$ affect the graph?

Tip:

In 3D graphing, understanding how each variable contributes to the shape of the surface can help you predict how the function behaves visually!