Piecewise functions are solved by graphing the various pieces of the function separately. This is done because a piecewise function acts differently at different sections of the number line based on the x or input value.
Know MoreThe function should be analyzed to determine the nature of the various pieces.
Step 1: Determine the value
Determine the value where x will be equal for all the pieces. This will be the dividing line between the different lines that represent the various pieces.
Step 2: Graph
Graph the various pieces in their own area of the number line.
Step 3: Solve
Solve for specific values by locating them on the graph.
Learn more about CalculusThe antiderivative of a trigonometric function is an alternative way of deducing the integral of the function, according to educators at Massachusetts Institute of Technology. The integral of the function is basically the derivative backwards. In the case of trigonometric functions, the antiderivative of a trigonometric identity is its derivative reverse.
Full Answer >Transformations of exponential functions occur when the function changes to shift the graph to the left, right, up, down or in reverse. An exponential function can be reversed by adding a negative sign in front of the exponent.
Full Answer >The inverse function of ln(x) is e^x, where e is the mathematical constant e = 2.718. One can easily check that these two functions are inverses of each other by noting that ln(e^x) = e^ln(x) = 1.
Full Answer >A latent function is an unintended or unrecognized consequence of an institution or social phenomenon. Unexpected negative consequences are typically called latent dysfunctions. School, for example, has the explicit, or manifest, function of educating individuals, but a latent function of teaching students about navigating social structures and relationships and keeping children off the streets for six to 10 hours a day.
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