Here are the essential concepts you must grasp in order to answer the question correctly.
Function Definition
A function is a relation that assigns exactly one output for each input from its domain. This means that for every x-value, there is a unique y-value. Understanding the definition of a function is crucial for determining whether a graph represents a function and whether it can have an inverse.
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Horizontal Line Test
The horizontal line test is a method used to determine if a function has an inverse that is also a function. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse that is a function. This test is essential for analyzing the graphs in the given exercises.
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Inverse Functions
An inverse function essentially reverses the effect of the original function. If a function f takes an input x to an output y, then its inverse f⁻¹ takes y back to x. For a function to have an inverse, it must be one-to-one, meaning it passes the horizontal line test, ensuring that each output corresponds to a unique input.
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