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Stitz-Zeager_College_Algebra_e-book

# We think back to arithmetic the reason r3 is undened

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Unformatted text preview: e following steps, in sequence 1. add 4 2. multiply by 3 Determine g (5) and ﬁnd an expression for g (x). Solution. Starting with 5, step 1 gives 5 + 4 = 9. Continuing with step 2, we get (3)(9) = 27. To ﬁnd a formula for g (x), we start with our input x. Step 1 produces x + 4. We now wish to multiply this entire quantity by 3, so we use a parentheses: 3(x + 4) = 3x + 12. Hence, g (x) = 3x + 12. We can check our formula by replacing x with 5 to get g (5) = 3(5) + 12 = 15 + 12 = 27 . Most of the functions we will encounter in College Algebra will be described using formulas like the ones we developed for f (x) and g (x) above. Evaluating formulas using this function notation is a key skill for success in this and many other math courses. Example 1.5.2. For f (x) = −x2 + 3x + 4, ﬁnd and simplify 1. f (−1), f (0), f (2) 2. f (2x), 2f (x) 3. f (x + 2), f (x) + 2, f (x) + f (2) Solution. 1. To ﬁnd f (−1), we replace every occurrence of x in the expression f (x) with −1 f (−1) = −(−...
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