The functions y = k/x and y = √x and their graphs
Plot a hyperbola from a table, find which quadrants its branches lie in, find k from a point and plot y = √x.
- Ukraine: grade 8
- Russia: grade 8
Guide
In the Ukrainian programme this is Grade 8 algebra: §1 item 10 "The function y = k/x and its graph" and §2 item 17 "The function y = √x and its graph".
Inverse proportion is y = kx with k ≠ 0. The domain is every number except 0. The graph is a hyperbola with two branches: in quadrants I and III when k > 0, in II and IV when k < 0. The points (a, b) and (-a, -b) lie on the graph together.
The function y = √x gives the side of a square of area x. Its domain and range are [0, ∞). The graph is in the first quadrant and starts at the origin.
First fill in the table, then plot the points on the plane.