Quick Check Solutions
Quick Check 1
Graphs \(A\) and \(C\) represent functions because they pass the vertical line test and each \(x\) value is paired with exactly one \(y\) value.
Quick Check 2
Quick Check 3
The inverse of graph \(B\) is a function because graph \(B\) passes the horizontal line test. Graphs \(A\) and \(C\) fail the horizontal line test, so their inverses are not functions.
Quick Check 1
Graphs \(A\) and \(C\) represent functions because they pass the vertical line test and each \(x\) value is paired with exactly one \(y\) value.
Quick Check 2
- Inverse functions are reflections of the graph over the line \(y=x\).
- The \((x,y)\) coordinates of inverse functions are switched.
- The domain of the original function becomes the range of the inverse function.
- The range of the original function becomes the domain of the inverse function.
Quick Check 3
The inverse of graph \(B\) is a function because graph \(B\) passes the horizontal line test. Graphs \(A\) and \(C\) fail the horizontal line test, so their inverses are not functions.