On the Subject of Function Identification

Does this module function as intended?

This needy module will show a random graph of a function upon activation. The defuser’s goal is to find the type of the function from the graph and submit it.

Controlling the module

• Use the left and right arrows at the bottom of the module to scroll through different types of functions.
• Click the function type to submit your answer.

The module will deactivate if you guess the function type correctly. Upon an incorrect submit, you will get a strike. The module will not deactivate.

Important information

• Only the types of functions listed below can appear on the module.
• Logarithmic functions are always in the form of $y={\log }_{a}x$, where $a>1$, to avoid confusion between logarithmic graphs and exponential graphs.
• Exponential functions are never in the form of $y=-a^x$ with $0\le a\le 1$, to avoid confusion between logarithmic graphs and exponential graphs.

Explanation

Type	Example graph	Description
Linear		Graphs of linear functions are straight lines, that go from top-right to bottom-left, or top-left to bottom-right. Their formula is $y=ax+b$.
Constant		Graphs of constant functions are straight lines parallel to the x axis. Their formula is $y=a$.
Reciprocal		Graphs of reciprocal functions form hyperbolas, which are curves with two parts. Their formula is $y=\frac{a}{x}+b$.
Quadratic		Graphs of quadratic functions are curves called parabolas, which are curves with only one part. Their formula is $y=a{x}^2+bx+c$.

Explanation

Type	Example graph	Description
Cubic		Graphs of cubic functions diverge to infinity on one side, and to negative infinity on the other. Their formula is $y=a{x}^3+b{x}^2+cx+d$.
Goniometric		Graphs of goniometric functions are odd. They are periodic and non-constant. This module takes their inverses as goniometric functions as well. You will not find any exponentially growing goniometric functions in this module. Their formula varies.
Exponential		Graphs of exponential functions are curves (there is only one curve) that grow exponentially. Their formula is $y=a{b}^x+c$.
Logarithmic		Graphs of logarithmic functions are curves very similar to exponential graphs. In fact, logarithmic functions are inverses of exponential functions. Their formula is $y=a{\log }_{b}x+c$.