Drawing Contour Maps: Level Curves of $f(x,y)=(y-2x)^2$

MHB
Thread starter ineedhelpnow
Start date Sep 29, 2014
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In summary, a contour map is a graphical representation of a function using lines or curves to connect points with the same value. To draw a contour map, you need to plot points with different values and connect them. The purpose of drawing contour maps is to visualize the shape and behavior of a function and identify critical points. Interpreting a contour map involves understanding the level curves, slope, and gradient of the function. However, contour maps have limitations in representing functions with discontinuities, multiple variables, and complex relationships.

Sep 29, 2014

ineedhelpnow

draw a contour map of the function showing several level curves $f(x,y)=(y-2x)^2$

how do i do this. i know i have $k=(y-2x)^2$ but how do i use it?

Last edited: Sep 29, 2014

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Sep 29, 2014

alyafey22

Gold Member

MHB

Use arbitrary positive values for $k$ and draw the resultant curve for each value.

Related to Drawing Contour Maps: Level Curves of $f(x,y)=(y-2x)^2$

1. What is a contour map?

A contour map is a graphical representation of a function, where the values of the function are represented by different lines or curves. These lines connect points with the same value, creating a map of the function's shape and level curves.

2. How do you draw a contour map?

To draw a contour map, you first need to determine the values of the function at different points. Then, plot these points on a graph and connect points with the same value. This will create the level curves of the function and give you the contour map.

3. What is the purpose of drawing contour maps?

Contour maps are useful in visualizing the shape and behavior of a function. They can also help in analyzing the relationship between the variables in the function and identifying critical points, such as maximum or minimum values, saddle points, and inflection points.

4. How can you interpret a contour map?

The contour lines on a contour map represent the level curves of the function, with each line representing a different value. The closer the lines are to each other, the steeper the slope of the function. The direction of the lines also indicates the direction of the gradient of the function at that point.

5. Are there any limitations to drawing contour maps?

Contour maps are limited in representing functions with continuous values. They may not be suitable for functions with discontinuities or sharp changes in values. Additionally, contour maps may not accurately represent functions with multiple variables and complex relationships between them.