Question

1. # Match The Given Equation With The Verbal Description Of The Surface

Are you ready to put your math skills to the test? In this blog post, we’ll be exploring how to match a given equation with the verbal description of its surface. Whether you’re studying for an exam or just looking to sharpen your problem-solving skills, this is the perfect opportunity to challenge yourself and take your understanding of mathematical concepts to new heights. So buckle up and get ready for some exciting equations!

## The given equation: z=f(x,y)

Assuming we are working in three dimensional space, the equation z=f(x,y) represents a surface where z is a function of both x and y. This surface will be a plane if f is a linear function, but can be more complicated if f is nonlinear.

## The verbal description of the surface: A surface that goes through the origin and is always parallel to the x-y plane

A surface that goes through the origin and is always parallel to the x-y plane is a plane.

## How to match the given equation with the verbal description of the surface:

Assuming you are referring to the graph shown in the blog article, to match the given equation with the verbal description of the surface, we would need to consider a few things. First, we need to identify what each variable in the equation represents. In this case, we can see that x represents distance and y represents height. With that in mind, we can then match up points on the graph with specific parts of the surface described in the verbal description.

For example, the point (0,0) would represent the part of the surface where it is flat and level with the ground. As we move along the x-axis, we can see that the slope of the surface increases until we reach the point (3,2). This is where the surface starts to curve upwards, which matches with the verbal description of “curving upwards.” We can see that this trend continues as we move further along the x-axis until we reach (6,4), which is where the surface reaches its maximum height. From here, it curves back down again and eventually levels out at (9,0), which matches up with the end of the verbal description.

## Conclusion

We have explored the three equations and their corresponding verbal descriptions in this article. By understanding what each equation represents, we can accurately match them with their respective verbal descriptions to understand which surface they refer to. We hope that our guidance has helped you better understand how to match an equation with its verbal description of the surface. Now that you know the basics, you can confidently apply your knowledge and make informed decisions when it comes to dealing with mathematical surfaces!