IB AA · 3A Concepts of a Function
Reflect a one-to-one graph in the line y = x.
Horizontal line test
An inverse exists when each y-value comes from only one x-value.
Swap coordinates
A point (a, b) on f becomes (b, a) on the inverse.
The mirror line
That swap is a reflection in y = x.
No inverse
If a horizontal line hits the graph twice, say that there is no inverse on this domain.
A straight graph.
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (1, 0), (5, 2), (9, 4).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (0, 0), (1, 1), (4, 3), (6, 5).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (6, 0), (3, 2), (0, 4).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (2, 1), (3, 2), (5, 4), (8, 6).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
A curve that may fail the horizontal line test.
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (−2, −1), (2, 1), (6, 3).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (0, 0), (2, 1), (3, 4), (5, 9).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (−1, 0), (1, 2), (4, 5).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
Decide, then sketch the reflection when it exists.
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (−3, −2), (0, 0), (3, 2).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (0, 1), (2, 2), (3, 4), (5, 8).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
The graph passes the horizontal line test, so an inverse exists.
Swap the coordinates of each labeled point.
The inverse points are (4, 0), (3, 1), (1, 3).
The inverse is the reflection of the graph in the line y = x.
Answer: inverse exists; reflect in y = x
A horizontal line meets this graph more than once.
One output comes from two inputs, so there is no inverse function on this domain.
Answer: no inverse function
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