Lesson 2: Evaluating FunctionsTo evaluate a function,1.Substitute the value in function of x.2.
Replace the all the variables with the number or expression for the func- tion’s variable.3.Evaluate and simplify the function.Example 1: Given the function: f(x ) = 2 x+ 1, nd f(6).Substitute 6 in place holder x,f(6) = 2 x+ 1Replace the all the variables with 6,f(6) = 2(6) + 1Then evaluate and simplify the function. f(6) = 12 + 1f (6) = 13Therefore, f(6) = 13.
It can also write in ordered pair which is (6,13).Example 2:Given the function f(x ) = x2+ 2 x+ 4 when x= 4.Substitute -4 in the place holder x,f ( 4) = x2+ 2 x+ 4Replace the all the variables with 6, f( 4) = ( 4) 2+ 2( 4) + 4Then evaluate and simplify the function.
f( 4) = (16) + ( 8) + 4f ( 4) = 12Therefore, f( 4) = 12 or simply as ( 4;12) :Example 3:1Giveng(x ) = x2+ 2 x- 1. Find g(2y).Answer in terms of y.g(2 y) = x2+ 2 x 1g (2 y) = (2 y)2+ 2(2 y) 1g (2 y) = 4 y2+ 4 y 1Therefore, 4( y)2+ 4 y 1:Example 4:Given f(x ) = 2 x2+ 4 x- 12, nd f(2 x+ 4).
Solution: f(2 x+ 4) = 2 x2+ 4 x 12= 2(2 x+ 4) 2+ 4(2 x+ 4) 12= 2(2 x+ 4)(2 x+ 4) + 4(2 x+ 4) 12= 2(4 x2+ 16 x+ 16) + 4(2 x+ 4) 12= (8 x2+ 32 x+ 32) + (8 x+ 16) 12Combine like terms f(2 x+ 4) = 8 x2+ (32 x+ 8 x) + (32 + 16 12)= 8 x2+ 40 x+ 36= 2(2 x2+ 10 x+ 9)Therefore, f(2 x+ 4) = 2(2 x2+ 10 x+ 9).Example 5:Given f(x ) = x2-x – 4. If f(a ) = 8, what is the value of a?Solution: Equate the function by x2-x 4 = 8x 2 x 4 = 8x 2 x 12 = 0( x 4)( x+ 3) = 0x 4 + 0; x+ 3 = 0x = 4; x= 3Therefore, the value of a can be either 4 or -3.2Exercises:Evaluate each functionGiven the functions:1.
k(x ) = x + 2, nd k(-5)2. p(x ) = 2 x, nd p(-4)3. g(n ) = n2+ 3, nd g(8)4. g(x ) = x3+ 5 x, nd g(5)5. h(n ) = n3+ 3 n2, nd h(-5)6.
w(a ) = a2+ 5 a, nd w(7)7. p(a ) = a3- 4 a, nd p(-6)8. h(n ) = 4 3n+ 8 5, ndh(-1)9. f(x) = -1 + 1 4x;nd f3 410. h(n) = n3+ 6 n, nd h(4)3Answers to Evaluating Functions Exercises:1.
112. -183. 674.
1505. -506. -147. -1928.
4 159. – 13 1610. 884
