Function Notation and Evaluating Functions Vocabulary Function Notation

Function Notation and Evaluating Functions

Vocabulary Function Notation Is a way to represent functions algebraically that makes it more efficient to recognize the independent and dependent variables. a way of writing a function. The most popular way to write a function is f(x). This is read “f of x” f(x)= is same as saying y= This tells you that x is the input/independent variable (This is NOT multiplying f times x. ) Example: f(x) output = 2 x + 4 input f(3) = 2(3) + 4 f(3) = 10 It is very similar to saying y = 2 x + 4 as we did in pre-algebra x is still input f(x) is the output instead of y Plug the x input 3 into the ‘rule’ 2 x+4 means with input 3, the function’s output is 10

How to use f(x)… f(x) = 2 x + 7, find f(5). This means to substitute 5 in where you see x and evaluate. f(5) = 2(5) + 7 f(5) = 17 The answer is 17. f(x) = -3 x 2 – x – 4, find f(2) This means to substitute 2 in where you see x. f(2) = -3(2)2 – 4 f(2) = -18

f(x) = 6 x – 3 If f(x) = 33, what does x equal? f(x) = 33 means the answer to 6 x – 3 is 33. Substitute 33 = 6 x – 3 36 = 6 x 6 33 where f(x) is. Now solve for x. =x The answer is that f(6) = 33.

Another example: Let X = {1, 2, 3, 4} and Y = {5, 6, 7, 8} f: X → Y Means the function is comprised of this set of ordered pairs f = {(1, 7), (2, 5), (3, 6), (4, 8)} What is f(2) ? f(2) = 5 since 2 is matched to 5. What is f(4) ? f(4) = 8 since 8 is matched to 4. If f(x) = 7, then what might x be? If f(x) = 7, then x = 1

Use a rule to create a function displayed in a table. Create a table using the domain {-2, -1, 0, 1, 2} for the rule f(x) = 2 x + 3. To do this, substitute each value of the domain into the rule (remember domain is the input/x values). Then add the answer to the table. x -2 -1 0 1 2 f(x) -1 1 3 5 7 f(-2) = 2(-2) + 3 f(-2) = -1 f(1) = 2(1) + 3 f(1) = 5 f(-1) = 2(-1) + 3 f(-1) = 1 f(2) = 2(2) + 3 f(2) = 7 f(0) = 2(0) + 3 f(0) = 3

Graph your table of values. x -2 -1 0 f(x) -1 1 3 1 2 5 7 Your table of values become ordered pairs of (x, f(x)). The ordered pairs are: (-2, -1), (-1, 1), (0, 3), (1, 5), (2, 7).

Use a rule to create a function displayed in a table. x -2 -1 0 1 2 f(x) 0 2 0

Graph your table of values. x -2 -1 f(x) 0 0 1 2 2 0

Write a function to represent the data in the table. Look at the x value. What operation or operations were used to change the x value to the f(x) value? Once you decide on a rule, make sure it works for the other x values. The rule is f(x) = x + 4.

Write a function to represent the data in table. Look at the x value. What operation or operations were used to change the x value to the f(x) value? Once you decide on a rule, make sure it works for the other x values. The rule is f(x) = x 2.

Write a function to represent the realworld scenario. The Museum of Science in Boston, MA has an exhibit called The Walk Through Computer. It is a scale model of a desktop computer. It is 20 times the size of a normal-sized desktop computer. Write a function rule to describe the relationship between the normal-sized computer and the size of the exhibit. f(x) = 20 x A space bar on a normal-sized computer is 4 3/8 inches long. How long is the space bar in the exhibit? f(35/8) = 20(35/8) f(35/8) = 87 ½ inches long Or about 7 ¼ feet