1111NotesSept26.pdf - September26,2017...

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Math 1111 Radical Functions 1 September 26, 2017 We've done Linear Functions, which couldn't have exponents. (Actually, they have exponents of 1.) For example, f ( x ) = 3 x + 5 We've done Quadratic Functions, which had an exponent of 2. For example, g ( x ) = x 2 + 6 x + 9 Now we are going to deal with functions with all sorts of exponents. Collectively, we will call them Power Functions. Examples: h ( x ) = x 5 + 2 x 3 + 1 j ( x ) = x 2/3 Fractional Powers and Radicals j ( x ) = x 2/3 Here are three ways to write the same function. You should be able to move back and forth between these ways. When written in this form, they are called Radical Functions.
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Math 1111 Radical Functions 2 September 26, 2017 Converting from Power to Radical The index of the root becomes the bottom of the fractional exponent. The exponent on the base becomes the top of the fractional exponent. The x had an understood 1 exponent. The square root ought to have a little "2" index, but we are usually lazy and don't write it. The simplest Radical Function: "The Square Root Function" Graph. Is it a function? Domain: Range: Extrema: x ­intercept: y ­intercept:
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