Concepts
This type of function matches each output with only one input.
A one-to-one function
If every output comes from exactly one input, this describes the function.
one-to-one function
What does it mean if every horizontal line touches a graph at most once?
The graph represents a one-to-one function.
This test uses horizontal lines to determine whether a function is one-to-one.
The Horizontal Line Test
Which function is more likely to have an inverse function: x^2 or x^3?
x^3
A graph shaped like an upward-opening parabola fails which graphical test?
The Horizontal Line Test.
Explain why a function that fails the Horizontal Line Test cannot have an inverse that is a function.
Because multiple inputs share the same output, causing the inverse to assign one input to multiple outputs
Name one way to make f(x)=x^2 one-to-one without changing its equation.
Restricting its domain (such as x≥0 or x≤0)
Without drawing the graph, explain how you could tell whether a function is likely to pass the Horizontal Line Test.
By determining whether it is always increasing or always decreasing, so no output is repeated.
A function must have this property before it can have an inverse that is also a function.
Being one-to-one
If f(3)=7 and f(8)=7, what conclusion can you make?
The function is not one-to-one.
A graph is increasing over its entire domain. What does this suggest about the Horizontal Line Test?
It will pass the test.