Evaluating functions
- 1. Evaluating Functions: To evaluate a function, substitute the input (the given number or expression) for the function's variable (place holder, x). Replace the x with the number or expression. 1. Given the function f (x) = 3x - 5, find f (4). Solution: Substitute 4 into the function in place of x. f (4) = 3(4) - 5 = 7. This answer can be thought of as the ordered pair (4,7). The answer may also be referred to as the image of 4 under f (x). 2. Find the value of h (b) = 3b2 - 2b + 1 when b = -3. Solution: Substitute -3 into the function in place of b. h (-3) = 3(-3)2 - 2(-3) + 1 = 34. 3. Find g (2w) when g (x) = x2 - 2x + 1. Solution: When substituting expressions, like 2w, into a function, using parentheses will help prevent algebraic errors. For this problem, use (2w). g (2w) = (2w)2 - 2(2w) + 1 = 4w2 - 4w +1 (Note: the answer is in terms of w.) 4. Given f (x) = 2x2 + 4x - 3, find f (2a + 3). Solution: Be sure to use parentheses! Be careful - more algebra work is needed here. f (2a + 3) = 2(2a + 3)2 + 4(2a + 3) - 3 = 2(4a2 + 12a + 9) + 8a + 12 - 3 = 8a2 + 24a + 18 + 8a + 12 - 3 = 8a2 + 32a + 27 Did you multiply? 5. Given f (x) = x2 - x - 4. If f (k) = 8, what is the value of k? Solution: Set the function rule equal to 8 and solve for k. x2 - x - 4 = 8 x2 - x - 12 = 0 (x - 4)(x + 3) = 0 x - 4 = 0; x + 3 = 0 x = 4; x = -3 The value of k can be either 4 or -3. To review on how to evaluate a function please click or copy the video link below to watch a video on how to evaluate a function. https://www.youtube.com/watch?v=PBimjTtsJQY (Evaluating a Function)