Math Example--Special Functions--Square Root Functions in Tabular and Graph Form: Example 31

Topic

Radical Functions

Description

This example illustrates the function y = -√(x) - 1. The graph shows a decreasing curve starting at (0, -1) and moving downward as x increases. A table lists x-values (0, 1, 3, 5, 7) with corresponding y-values of -1, -2, -2.732, -3.236, and -3.646. Students are asked to create a table of x-y coordinates and graph the function.

This example introduces students to a negative square root function with a vertical shift. It helps them understand how the negative sign outside the square root and the subtraction of 1 affect the shape and position of the graph. By comparing this to previous examples, students can visualize how these changes impact 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. This approach helps students recognize patterns and relationships between equations and their graphs, fostering critical thinking and analytical skills.

Teacher's Script: Let's examine the function y = -√(x) - 1. How do you think this graph will differ from our previous examples? We'll use x-values of 0, 1, 3, 5, and 7. Notice how the y-values are all negative and decreasing. When we plot these points, we see that our curve starts at (0, -1) and decreases as x increases. Can anyone explain why this happens? How does the negative sign outside the square root and the subtraction of 1 affect the function's behavior?

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