Graphs and Corresponding Equations: Functions Overview

Study Notes

Graphs and Corresponding Equations

y = x^3: Represents a cubic function characterized by an S-shaped curve. It passes through the origin and has inflection points where the curve changes concavity.
y = 1/x^2: Depicts a rational function, specifically a hyperbola. It approaches the x-axis asymptotically, never touching it, and is always positive for x ≠ 0.
y = 1/x: Another rational function representing a hyperbola. It has vertical and horizontal asymptotes at x = 0 and y = 0 respectively, and it approaches these lines but never intersects them.
y = x: Linear function illustrated by a straight line with a slope of 1. It bisects the first and third quadrants, indicating a direct proportional relationship between x and y.
y = |x|: Absolute value function visualized as a V-shaped graph. It is symmetric around the y-axis, with a vertex at (0,0) and slopes of 1 and -1 in the first and second quadrants respectively.
y = x^2: Quadratic function with a U-shaped parabolic curve. It opens upwards, has its vertex at the origin, and is symmetric about the y-axis.
y = sqrt(x): Represents a square root function characterized by a gradual increase. Defined only for x ≥ 0, it starts at the origin and rises to the right, never touching the negative side of the axes.
y = 3sqrt(x): A scaled version of the square root function, amplifying the rise of the graph. Like y = sqrt(x), it only exists for x ≥ 0 and has a steeper slope due to the multiplier of 3.

Description

Explore different mathematical functions including linear, quadratic, cubic, and rational functions through their corresponding graphs. This quiz tests your understanding of how these equations represent various shapes and properties in mathematics.