Name Date Class. You can also write equations for functions that are described in words. The length of the pool is 6 times the width of the pool.

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1 Name Date Class Review for Mastery: Tables and A function is a rule that relates two quantities so that each input value corresponds to exactly one output value. In the table below, the x-values are the input and the y-values are the output. To write an equation for a table of values, x first compare the x- and y-values to find a y ? pattern. Each y-value is 4 more than its corresponding x-value. Then use the pattern to write a rule for the table. y = x + 4 You can use the rule to find a missing value in a table. y = x + 4 To find the value of y in the table above when x = 7, substitute y = for x in the equation. y = 11 So y is 11 when x is 7. Write an equation for a function that gives the values in each table. Use the equation to find the value of y for the indicated value of x. 1. x y ? x y ? _ You can also write equations for functions that are described in words. The length of the pool is 6 times the width of the pool. l = length of pool w= width of pool l = 6w Choose variables for the equation. Write an equation. Write an equation for the function. Tell what each variable you use represents. 3. Todd is 6 inches taller than Scott. 4. Alana is 4 times as old as Tracey. _

2 Name Date Class Review for Mastery: Graphing You can express solutions to equations as ordered pairs. To express solutions to y = x 3 as ordered pairs, substitute the given values for x in the equation. Then write the solutions as ordered pairs. x x 3 y ordered pair (x, y) (9, 6) (7, 4) (5, ) (3, 0) Use the given x-values to write solutions to y = x as ordered pairs. 1. x x Y ordered pair (x, y) You can check whether an ordered pair is a solution to an equation by substituting the x- and y-values into the equation. Is (, 3) a solution to y = x + 1? y = x + 1 Write the equation. 3 = + 1 Substitute 3 for y and for x. 3 = 3 So (, 3) is a solution to y = x + 1. Determine whether each ordered pair is a solution to the given equation.. (1, 4); y = 4x 3. (3, 1); y = x 3 4. (, 8); y = x + 4

3 Name Date Class Review for Mastery: Slope and Rate of Change The rate of change of a function is a ratio that compares the difference in y-values to the difference in x-values. On a straight line this ratio is constant, and it is possible to give the rate of change, or slope, of the entire line by only looking at two points. To find rates of change in a table, first pick two consecutive data points and find the difference between them. In the following table, find the difference between the second and third x- and y-values. x 0 4 y = 6 3 = 3 Next, write a ratio comparing the difference in y-values to the difference in x-values: 6 3 = 3 4 The rate of change between these points is 3. If you repeat this process for all pairs of data points in the table above, you will find that the rate of change is always 3. When we graph the points from this table they will form a straight line with a slope of 3, as shown. To determine the slope of a line from its graph, pick two points from the line, and write the rate of change ratio using the same process as above. Find each rate of change. 1.. x y x y 1 4 6

4 Name Date Class Review for Mastery: Inequalities An equation is a statement that says two quantities are equal. An inequality is a statement that says two quantities are not equal. The chart shows symbols and phrases that indicate inequalities. < > Less than Fewer than Below Greater than More than Above Less than or equal to At most No more than Greater than or equal to At least No less than Complete the inequality for each situation. 1. No more than 00 people can be seated in the restaurant. number of people seated in restaurant 00. The waiting time for a table is at least 0 minutes. waiting time 0 minutes 3. The price of all special dinner entrees is below $10. special dinner entrees $10 4. The Yoshida family spent more than $40 for dinner. Yoshida family spent $40 An inequality can be shown on a graph. The graph shows: Inequality Graph All numbers greater than 3 All numbers greater than or equal to 3 All numbers less than 3 All numbers less than or equal to 3 x > 3 x 3 x < 3 x 3 The open circle at 3 shows that the value 3 is not included in the graph. The closed circle at 3 shows that the value 3 is included in the graph.

5 Name Date Class Review for Mastery: Inequalities (continued) Graph each inequality. 5. x > 4 Draw an open circle at 4. Read x > 4 as x is greater than 4. Draw an arrow to the right of x 1 Draw a closed circle at 1. Read x 1 as x is less than or equal to 1. Draw an arrow to the left of a > 1 8. y 3 A compound inequality is a combination of two inequalities. The graph shows: Inequality Graph All numbers from to x All numbers greater than or less than x > or x < Graph each compound inequality < x 3 Draw an open circle at 0 and a closed circle at 3. Shade the line between 0 and x 4 or x 1 Draw a closed circle at 1 and a closed circle at 4. Shade the line to the left of 1 and to the right of 4.