Module 22
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| What is an one-to-one function? | A one-to-one function is when each x-value corresponds to only 1 y-value, and each y-value corresponds to only 1 x-value.
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| How can you check on a graph if an equation is an one-to-one function? | You can do horizontal line test. If every horizontal line intersects only once, then the function is a one-to-one function.
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| What type of lines are one-to-one functions? | All lines are one-to-one functions except for horizontal or vertical lines.
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| What is the inverse to an one-to-one function? | The inverse of an one-to-one function f(x) is f^-1 that consists of all ordered pairs (y,x), while f consists of (x,y).
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| What are the steps to finding the inverse of an one-to-one function f(x)? | Step 1: Replace f(x) with y
Step 2; Change x to y and y to x
Step 3; Solve the equation for y
Step 4; Replace y with the notation f^-1(x)
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| Is there a way to check if f(x) is an one-to-one function? | Yes, if f(x) is an one-to-one function, then the inverse of f(x) is the function f^-1. Or where (f^-1 o f)(x)=x and (f o f^-1)(x)=x
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Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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