Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 36

Topic

Radical Functions

Description

This example illustrates the function y = -√(x + 1) - 1. The graph shows a downward curve starting at (0, -2) and moving downward as x increases. A table lists x-values (0, 1, 3, 5, and 7) with corresponding y-values of -2, -2.414, -3, -3.449, and -3.828. Students are asked to create a table of x-y coordinates and graph the function.

This example introduces students to square root functions with both a constant term inside and outside the radical, combined with a negative sign. It helps them understand how these factors affect the shape of the graph and its vertical shift. By comparing this to previous examples, students can visualize how adding constants inside and outside the square root affects the function's behavior.

Providing multiple examples with different variations is essential for deepening students' understanding of square root functions. Each example builds on previous knowledge, challenging students to apply what they've learned in new contexts.

Teacher's Script: Let's examine the function y = -√(x + 1) - 1. How do you think this graph will compare to our previous examples? We'll use x-values of 0, 1, 3, 5, and 7. Notice how the y-values change as we plot these points. The curve starts at (0, -2) and moves downward more steeply than some of our earlier examples. 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.