2_Evaluating_Fungggggggggggggggsdctions.pptx

gdshjfhw4q

1. EVALUATING FUNCTIONS

2. Law of Substitution If a + x = b and x = c, then a + c = b Illustration: To find the value of n 2 when n is 15: Substitute 15 in place of n in n 2 to get 15 2 or 225.

3. Evaluating Functions To evaluate function is to replace its variable with a given number or expression. Think of the domain as the set of the function’s input values and the range as the set of the function’s output values as shown in the figure below. The input is represented by x and the output by f(x).

4. Example 1 If f(x) = x + 8, evaluate each. f(4) f(–2) f(–x) f(x + 3)

5. SOLUTION TO EXAMPLE 1 f(4) = 4 + 8 or 12. f(–2) = –2 + 8 or 6 f(–x) = –x + 8 f(x + 3) = x + 3 + 8 or x + 11

6. EXAMPLE 2 The price function p(x) = 640 – 0.2(x) represents the price for which you can sell x printed T-shirts. What must be the price of the shirt for the first 3 entries in the table? Target No. of Shirt Sales 500 900 1300 1700 2100 2500 Price per T-shirt

7. SOLUTION TO EXAMPLE 2 p(500) = 640 − 0.2(500) = 640 − 100 = 540 p(900) = 640 – 0.2(900) = 640 – 180 = 460 p(1 300) = 640 − 0.2(1 300) = 640 − 260 = 380

8. EVEN AND ODD FUNCTIONS The function f is an even function if and only if f(–x) = f(x), for all x in the domain of f . The function f is an odd function if and only if f(–x) = –f(x), for all x in the domain of f .

9. Example 3 Identify each function as even, odd, or neither. f(x) = x 5 g(x) = 3x 4 – 2x 2 h(x) = x 2 + 3x + 1

10. SOLUTION TO EXAMPLE 3 f(x) = x 5 Since f(–x) = –f(x), f(–x) = (–x) 5 f is an odd function. = –x 5 g(x) = 3x 4 – 2x 2 Since g(–x) = g(x), g(–x) = 3(–x) 4 – 2(–x) 2 g is an even function. = 3x 4 – 2x 2

11. SOLUTION TO EXAMPLE 3 h(x) = x 2 + 3x + 1 h(–x) = (–x) 2 + 3(–x) + 1 = x 2 – 3x + 1 Only the second term changed sign when x was replaced by –x. Thus, h is neither even nor odd.

12. EXERCISE A Evaluate each function at the indicated values of the independent variable and simplify the result. f(x) = 9 – 6x f(–1) g(x) = x 2 – 4x g(2 – x) h(x) =2x h ( ) f(x) = –2x 2 – 3 f(–3) f(x) = √9 − x 2 f(3)  

13. EXERCISE B The function C described by C(F) = 5/9(F − 32) gives the Celsius temperature corresponding to the Fahrenheit temperature F. Find the Celsius temperature equivalent to 14°F. Find the Celsius temperature equivalent to 68°F.

14. EXERCISE C Determine whether or not each function is even , odd , or neither . f(x) = g(x) = h(x) = h(x) = g(x) =