Transcription of Nonlinear Functions - UH
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Nonlinear Functions - UH
Nonlinear Functions By definition, Nonlinear Functions are Functions which are not linear. Quadratic Functions are one type of Nonlinear function. We discuss several other Nonlinear Functions in this section. A. Absolute Value Recall that the absolute value of a real number x is defined as if 0if x<0xxxx = Consequently, the graph of the function ()fxx= is made up of two different pieces. For x > 0, the graph is the graph of the linear function x, and for x < 0, the graph is the graph of the linear function x . We show the three different graphs below. ()fxx= for x > 0 ( )fxx= for x < 0 ()fxx= The graph of ()gxx= can be obtained from the graph of ()fxx= by reflecting the graph across the x axis.
xxxx x xxxx ⎧ −−≥⎧ − −≥ −= =⎨⎨ ⎩−− −<⎩− +−< We can solve the inequality 210x−≥ as follows. 1 210 2 1 2 xxx−≥ ⇔ ≥ ⇔ ≥ If we combine this information with the definition of g, we have 2 f/211i 2 1 2 f/ 211i xx gx x xx ⎧ −≥ =−=⎨ ⎩−+ < So, g is a piecewise function, made up of two ...
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