Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 2

Topic

Radical Functions

Description

This example demonstrates the function y = √(2x). The graph shows an increasing curve starting at the origin (0, 0) and rising more steeply than y = √(x) as x increases. A table lists x-values (0, 1, 3, 5, and 7) with their corresponding y-values, and points on the graph are plotted based on these coordinates. Students are asked to create a table of x-y coordinates and graph the function y = √(2x), with x-values of 0, 1, 3, 5, and 7 and corresponding y-values of 0, 1.414, 2.449, 3.162, and 3.742.

This example builds on the previous one, introducing a coefficient inside the square root. It helps students understand how this coefficient affects the shape and steepness of the graph. By comparing this function to y = sqrt(x), students can visualize the impact of the coefficient 2 on the function's behavior.

Providing multiple examples with slight variations is essential for deepening students' understanding. It allows them to make connections between different forms of square root functions and develop a more intuitive grasp of how changes in the equation affect the graph. This approach fosters critical thinking and analytical skills.

Teacher's Script: Now, let's look at the function y = √(2x). How do you think this graph will compare to our previous example of y = √(x)? Let's create our table of x-y coordinates using the same x-values as before: 0, 1, 3, 5, and 7. Notice how the y-values are larger this time. When we plot these points, we can see that this curve rises more steeply than our previous example. Can anyone explain why this happens?

For a complete collection of math examples related to Radical Functions click on this link: Math Examples: Square Root Functions Collection.