Math Problem Statement
Which of the following functions is graphed below?
Solution
The graph shown in the image resembles the function of a cubic curve. Here's how we can identify it:
- The graph passes through the origin , which is a characteristic of the cubic function.
- The curve shows symmetry around the origin, and its general shape looks like an increasing S-curve, which matches the form of .
- The curve also extends down to the left (negative x-values) and up to the right (positive x-values), which is another typical trait of a cubic function.
So, the correct answer from the options given is: Cube
Would you like more details or have any other questions?
Here are 5 follow-up questions related to this topic:
- What is the general equation of a cubic function?
- How do cubic functions differ from quadratic functions in terms of graph shapes?
- Can a cubic function have multiple inflection points?
- What transformations can you apply to a cubic function?
- How do you find the critical points of a cubic function?
Tip: When identifying graphs, focus on key features like symmetry, turning points, and behavior at the extremes to distinguish between different types of functions.
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Math Problem Analysis
Mathematical Concepts
Graphing Functions
Cubic Functions
Algebra
Formulas
y = x^3
Theorems
Cubic Function Properties
Suitable Grade Level
Grades 9-12