Student Page Algebra/ Da #4 90 Minute Class Functions, Patterns and X-Y Tables Definition: A relation is an set of ordered pairs Ex: # {(,), (-7,6), (-,4)} # { (0,8), (-, ), (0,6)} Definition: A function is a special relation where each element of the domain is paired with exactl one element of the range (for each value of x there is one and onl one value of ) In the examples above, # is a function, while # is not (an input value of 0 has an output value of 8 and 6, therefore not a function) Domain: the set of input values or x s Range: the set of output values or s (what ou get from the function when ou put in a value of x.) The domain for the function {(,), (-7,6), (-,4)} is {-7,-,}. (Place them in least to greatest order, duplicates do not have to be repeated) The range for the function {(,), (-7,6), (-,4)} is {,4,6}. (Place them in least to greatest order, duplicates do not have to be repeated) Function notation: Read f(x) as f of x To evaluate a function, take the value specified and replace the variable in the function with the value from x. Then perform the math operations specified to get the output. (This is sometime thought of as the value of ) Ex : Let f(x) = x 7, find: f(-) = (substitute in for x) f(-) = (-) -7 = - -7 = -9 So f(-) = -9
Using an X-Y table to write an equation A. Determine a relationship between the x- and -values. Write an equation. x 4 - - 0 Step : List possible relationships between the first x- and -values. = - or (-) = - Step : Determine if one relationship works for the remaining values. =- (-) - = 0 (-) 0 4 = 4 (-) The first relationship works. The value of is less than x. Step : Write an equation: = x - (The value of is less than x.) B: Determine a relationship between the x- and -values in the relation: x 4 6 9.Write an equation that shows the relationship. Y=X The equations in both Example A and B describe a function because for each x- value (input), there is onl one -value ( output). Vertical line test: Ever point on a vertical line has the same x-coordinate, so a vertical line cannot represent a function. If a vertical line passes through more than one point on the graph of a relation, the relation must have more than one point with the same x-coordinate. Therefore the relation is not a function. Use the vertical-line test to determine whether the graph below is a function. If not, identif two points a vertical line would pass through. 5 4 5 4 4 5 x 4 5 Not a function. Two points a vertical line would pass through are (0,) and (0,-)
Multiple Choice: Point. Which of the following is a function? A. {(,) (7,) (-,) (5,)} C. {(,6) (,-7) (6,) (,7)} B. {(-4,6) (-7,) (5,-) (-4,7)} D. {(,6) (,-7) (,-6) (-,7)}. Which equation shows the relationship between the X and Y values in the following table: x 4 5-5 -4 - - A. Y = X 7 C. Y = X-7 B. Y = -5X D. Y = 7 X. Which equation shows the relationship between the X and Y values in the following table: x 4 5 5 7 9 A. Y = X + C. Y = X- B. Y = X+ D. Y = X- 4. Which of the following values represents f(x) = x evaluated at. A. 0 C. 9 B. 7 D. 6 5. Which of the following values represents f(4) for f(x) = x - A. 0 C. 9 B. 7 D. 6
Free Response: Points Is the following a graph of a function? If not, identif two points a vertical line would pass through x Free Response: Points Is the following a graph of a function? If es, show wh. If not, identif two points a vertical line would pass through x It is a function.
Free Response: 4 Points For the following relation in the table: x 6 9 - -. Determine the domain. Determine the range. Determine if the relation is a function 4. Write an equation for the relation Free Response: 4 Points For the following relation in the table: x 6 0 8-0 -4-6. Determine the domain. Determine the range. Determine if the relation is a function and explain wh 4. Write an equation for the relation
Answer Page Multiple Choice: Point A. Which of the following is a function? A. {(,) (7,) (-,) (5,)} C. {(,6) (,-7) (6,) (,7)} B. {(-4,6) (-7,) (5,-) (-4,7)} D. {(,6) (,-7) (,-6) (-,7)} A. Which equation shows the relationship between the X and Y values in the following table: x 4 5-5 -4 - - A. Y = X 7 C. Y = X-7 B. Y = -5X D. Y = 7 - X C. Which equation shows the relationship between the X and Y values in the following table: x 4 5 5 7 9 A. Y = X + C. Y = X- B. Y = X+ D. Y = X- B 4. Which of the following values represents f(x) = x evaluated at. A. 0 C. 9 B. 7 D. 6 D 4. Which of the following values represents f(4) for f(x) = x - A. 0 C. 9 B. 7 D. 6
Free Response: Points Is the following a graph of a function? If not, identif two points a vertical line would pass through x Not a function. (0,), (0,-) Free Response: Points Is the following a graph of a function? If es, show wh. If not, identif two points a vertical line would pass through x It is a function. Draw a vertical line anwhere and it will onl pass through the graph once.
Free Response: 4 Points For the following relation in the table: x 6 9-0 6. Determine the domain. Determine the range. Determine if the relation is a function and explain wh 4. Write an equation for the relation D: {,6,9,} R: {-,0,,6 } It is a function. Onl one value of for each x (partial credit if the sa no value of x is repeated.) Y = X - 6 _ Free Response: 4 Points For the following relation in the table: x 6 0 8-0 -4-6. Determine the domain. Determine the range. Determine if the relation is a function and explain wh 4. Write an equation for the relation D: {6,0,8,} R: {-6,-4,0,- } It is a function. Onl one value of for each x (partial credit if the sa no value of x is repeated.) =