Compare Properties of Two Functions: CCSS.Math.Content.8.F.A.2

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8th Grade Math › Compare Properties of Two Functions: CCSS.Math.Content.8.F.A.2

Questions 1 - 10

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 1.11.15 pm

$\textup{Table, }7$

$\textup{Table, }5$

$\textup{Equation, }6$

$\textup{Equation, }7$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

An input/output table displays sets of ordered pairs. The input column represents the x-values and the output column represents the y-values. We can select two sets of ordered pairs from the table to solve for the slope:

$\frac{15-8}{5-4}=\frac{7}{1}=7$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

The function with the greatest rate of change will possess the greatest slope. In this case, the greater slope is , which was displayed in the function written in table form; thus, the following answer is correct:

$\textup{Table, }7$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 11.59.17 am

$y=\frac{1}{3}x-4$

$\textup{Table, }\frac{1}{2}$

$\textup{Table, }\frac{3}{4}$

$\textup{Equation, }\frac{1}{2}$

$\textup{Equation, }\frac{1}{3}$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{10-9}{8-2}=\frac{1}{2}$

The slope for our table is $\frac{1}{2}$

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is $\frac{1}{3}$

The function with the greatest rate of change will possess the greatest slope. In this case, the greater slope is $\frac{1}{2}$ , which was displayed in the function written in table form; thus, the following answer is correct:

$\textup{Table, }\frac{1}{2}$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 11.40.24 am

$\textup{Table, }5$

$\textup{Table, }10$

$\textup{Equation, }4$

$\textup{Equation, }2$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{9-(-1)}{3-1}=\frac{10}{2}=5$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }5$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 8.52.05 am

$\textup{Equation, }9$

$\textup{Table, }9$

$\textup{Equation, }6$

$\textup{Table, }3$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{12-3}{4-1}=\frac{9}{3}=3$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

The function with the greatest rate of change will possess the greatest slope. In this case, the greater slope is , which was displayed in the function written in equation form; thus, the following answer is correct:

$\textup{Equation, }9$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 11.50.11 am

$\textup{Equation, }1$

$\textup{Equation, }2$

$\textup{Table, }1$

$\textup{Table, }\frac{1}{3}$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{5-4}{6-3}=\frac{1}{3}$

The slope for our table is $\frac{1}{3}$

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Equation, }1$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 1.54.16 pm

$\textup{Table, }5$

$\textup{Table, }10$

$\textup{Equation, }5$

$\textup{Equation, }10$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{62-37}{10-5}=\frac{25}{5}=5$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }5$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 12.03.31 pm

$\textup{Table, }4$

$\textup{Table, }6$

$\textup{Equation, }4$

$\textup{Equation, }2$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{4-0}{5-4}=\frac{4}{1}=4$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }4$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 1.50.59 pm

$\textup{Equation, }9$

$\textup{Equation, }6$

$\textup{Table, }10$

$\textup{Table, }6$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{9-3}{3-2}=\frac{6}{1}=6$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

The function with the greatest rate of change will possess the greatest slope. In this case, the greater slope is , which was displayed in the equation written in table form; thus, the following answer is correct:

$\textup{Equation, }9$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 8.52.05 am

$\textup{Table, }3$

$\textup{Table, }2$

$\textup{Equation, }4$

$\textup{Equation, }2$

Explanation

The rate of change is also known as the slope. As we have learned we can use the following equation to solve for the slope of the table:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\frac{12-3}{4-1}=\frac{9}{3}=3$

The slope for our table is

In order to determine the slope of the equation, we need to make sure the equation is in slope-intercept form:

In this equation, the variables and are defined as the following:

$\textup{m=slope}$

$\textup{b=y-intercept}$

The given formula for this problem was provided in slope-intercept form; thus, the slope for the equation is

$\textup{Table, }3$

The table and the equation provided represent two different functions. Which of these two functions—either table or equation form—has the greater rate of change, and what is the rate of change?

Screen shot 2016 03 14 at 11.50.11 am