Contour Maps and Function Values

The video tutorial explains how to use contour maps to estimate function values. It introduces contour maps, describes the properties of contour lines, and demonstrates how to estimate function values at specific points using these lines. The tutorial provides examples and emphasizes the importance of estimation due to the difficulty of exact calculations.

What do contour maps represent in terms of functions?

• The slope of a function

• The points where the function values are the same

• The maximum value of the function

• The points where the function is undefined

How are the contour lines oriented on a contour map?

• They are perpendicular to each other

• They form concentric circles

• They intersect at the origin

• They are parallel and equidistant

What happens to the function values as you move perpendicular to the contour lines?

• They fluctuate randomly

• They increase at a constant rate

• They remain the same

• They decrease at a constant rate

What is the first step in estimating the function value at a given point using a contour map?

• Find the midpoint of the contour lines

• Draw a tangent line at the point

• Locate the point on the coordinate plane

• Calculate the slope at the point

If a point is close to a contour line with a function value of 120, what can be inferred about the function value at that point?

• It is exactly 120

• It is slightly more than 120

• It is slightly less than 120

• It is exactly 160

For the point (1, 10), which contour line is it closest to?

• Contour line with value 80

• Contour line with value 120

• Contour line with value 160

• Contour line with value 40

What is the estimated function value for the point (4, 15)?

• 175

• 200

• 160

• 180

Why is it difficult to be exact with function values on a contour map?

• Because the map is not to scale

• Because the estimation is based on proximity to contour lines

• Because the function values are not labeled

• Because the contour lines are not visible

What is the function value halfway between contour lines of 160 and 200?

• 180

• 190

• 170

• 160

What is the purpose of estimating function values on a contour map?

• To determine the maximum value of the function

• To find the exact value of the function

• To calculate the derivative of the function

• To understand the general trend of the function