Applying the Horizontal Line TestSee LarsonPrecalculus.com for an interactive version of this type of example.a. The graph of the function f(x) = x3 − 1 is shown in Figure P.63. No horizontal lineintersects the graph of f at more than one point, so f is a one-to-one function anddoes have an inverse function.b. The graph of the function f(x) = x2 − 1 is shown in Figure P.64. It is possible tofind a horizontal line that intersects the graph of f at more than one point, so f isnot a one-to-one function and does not have an inverse function.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Applying the Horizontal Line Test
See LarsonPrecalculus.com for an interactive version of this type of example.
a. The graph of the
intersects the graph of f at more than one point, so f is a one-to-one function and
does have an inverse function.
b. The graph of the function f(x) = x2 − 1 is shown in Figure P.64. It is possible to
find a horizontal line that intersects the graph of f at more than one point, so f is
not a one-to-one function and does not have an inverse function.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
