Radical Functions
Radical functions involve variable expressions with non-integral exponents. Some examples of radical functions are shown below.
Consider the following problem:
Problem: Two cars are travelling towards an intersection from different directions. One car is 10 km north of the intersection and is travelling south at 20 km/h. The other car is 20 km west of the intersection and is travelling east at 10 km/h. Write a function to represent the distance between the two cars.
- After 15 minutes, how far is each car from the intersection? How is the Pythagorean Theorem useful in solving this problem?
- Use the distance formula to determine the distance between the cars in 15 minutes.
- If you plotted the time versus the distance between the two cars, what do you think your graph will look like?
Explore this problem using the interactive below.
- Explore how the graph of the distance between the two cars changes as we vary the starting position and speed of each car by moving the red and black sliders on the right. Notice that the graph represents a radical function.
- What was the shape of the graph of time versus distance between the two cars? Draw a sketch.
- How does your sketch explain what is happening to the distance between the two cars over time?
- Give 2 examples of radical functions.
See the matching Ontario Mathematics Curriculum expectations.