Other graphs · Grade 11
In Grade 11 you learn: the circle x² + y² = r².
Beyond straight lines and parabolas, a few graph shapes turn up again and again: cubics like y = x³, reciprocals like y = 1/x, exponentials like y = 2ˣ, and circles x² + y² = r². Recognizing them from their equations, and sketching them, is useful in science and finance as well as math.
Key facts
- Cubic y = x³ + …: an S-shaped curve that can cross the x-axis up to three times.
- Reciprocal y = k/x: two separate branches that get closer and closer to the axes (asymptotes) but never touch them.
- Exponential y = aˣ with a > 1: passes through (0, 1), grows faster and faster, and never goes below the x-axis.
- Circle x² + y² = r²: center (0, 0) and radius r.
- To plot any graph, make a table of values, plot the points and join them with a smooth curve.
Worked examples
Example 1
Find the radius of the circle x² + y² = 49. Is the point (5, 5) inside or outside it?
Answer: Radius 7; outside