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.
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.
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.
Applying the Horizontal Line Test See 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 line 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.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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