Which variable is dependent? The student provides no explanation. For examples such as in the first part, a question might come up along the lines of "Could we define a function using other letters in the word? Do you notice a pattern? What does it mean when n increases by one? Questions Eliciting Thinking How are the numbers on the left side of the table related to the numbers on the right side of the table?
Provide additional problem contexts that can be modeled by an equation in two variables. Either the set from which the input is taken can be modified to be words with at least three letters. Show the student how to check each row and be certain the mathematical relationship is consistent for every input value.
Questions Eliciting Thinking Which variable is independent dependent? Can you determine how much the grade changes for each right question? What happens to the number of diagonals when the number of sides changes?
How is the dependent variable related mathematically to the independent variable? Change in the dependent variable depends on change in the independent variable.
What happens to g when n increases by one? Instructional Implications Ask the student to identify the independent and dependent variables and to verbally describe the relationship between them. IM Commentary The purpose of this task is to connect the a function described by a verbal rule with corresponding values in a table one of six connections to be made between the four ways to represent a function, the other two being through its graph and through an expression.
Explain that typically the value of the independent variable is freely chosen, but the value of the dependent variable is calculated for particular values of the independent variable. Can you relate the amount of change in the number of sides to the change in the number of diagonals?
Questions Eliciting Thinking Can you write an equation that uses both variables? The task brings to mind one function which is of more value as a brain teaser than of mathematical value. Students who think they have found the rule could either describe it, or perhaps supply input-output pairs which follow the rule they are guessing.
Ask the student to distinguish dependent from independent variables given in equations, written descriptions, and real-world situations. Clarify that both the dependent and independent variables change, though in different ways. Examples of Student Work at this Level The student recognizes the relationship between independent and dependent variables but does not write an accurate equation.
Have the student determine whether the value of the dependent variable increases or decreases as the value of the independent variable increases. Explain to the student how the equation shows the relationship between the variables. Then encourage the student to analyze the relationship more closely and describe the actual amount of change by referring to numerical values and operations.
Records the operation instead of the complete equation. Clarify the difference between expressions and equations.
What is needed in either case is an analysis of whether the chosen rule is appropriate and whether there are other reasonable rules.
Will your equation work for every input value?Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
A table of values shows a list of the values for an independent variable, x, matched with the value of the dependent variable, y.
In many cases, an equation can be used to relate the two values. If you know the equation, you can easily generate a table of values. If the table has a quadratic function rule, for the corresponding value.
This check passes since and. Calculate the value of such that when,, and. Identify the independent and dependent variables in each situation.
Then use function notation to express each relationship.: the size of the drain (independent variable) Write a rule that expresses the relationship for each pair of input and output values in each table.
xy 0 0 ab 0 0. Example 6: Write a function rule to represent each situation. A) the total cost C for pounds of copper if each pound costs $ B) the amount of your friend's allowance if the amount she recieves is.
1. Complete the function table. 2. Write the rule of the function table, using words. 3. pairs to plot and label each point. Then use a ruler and draw a segment to connect the points.
6. Compare the y-coordinate of each point to its Write the rule of the function table, using words. 3.Download