함수 전체 문제

For the following exercises, use the graph in (the referenced figure) showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$10,000 and ending at 2005 at$4,000. The x-axis ranges from 0 to 30 in intervals of 5 and the y –axis goes from 0 to 12,000 in intervals of 2,000." loading="lazy" decoding="async">

Find the linear function y, where y depends on $x,$ the number of years since 1980.

For the following exercises, use the graph in (the referenced figure) showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$10,000 and ending at 2005 at$4,000. The x-axis ranges from 0 to 30 in intervals of 5 and the y –axis goes from 0 to 12,000 in intervals of 2,000." loading="lazy" decoding="async">

Find and interpret the y-intercept.

For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in (the referenced table). Assume that the house values are changing linearly.

Year	Pima Central	East Valley
1970	32,000	120,250
2010	85,000	150,000

In which subdivision have home values increased at a higher rate?

For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in (the referenced table). Assume that the house values are changing linearly.

Year	Pima Central	East Valley
1970	32,000	120,250
2010	85,000	150,000

If these trends were to continue, what would be the median home value in Pima Central in 2015?

Find the slope of the line in (the referenced figure).

Write an equation for line in (the referenced figure).

Does (the referenced table) represent a linear function? If so, find a linear equation that models the data.

Does (the referenced table) represent a linear function? If so, find a linear equation that models the data.

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular.

Sketch a line with a y-intercept of $(0,5)$ and slope $-\frac{5}{2}.$

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular.

Graph of the linear function $f(x)=-x+6.$

For the following exercises, use the graph in (the referenced figure), showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$15,000 to 2010 at about$32,500. The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 0 to 35,000 in intervals of 5,000." loading="lazy" decoding="async">

Find the linear function $y,$ where $y$ depends on $x,$ the number of years since 1980.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$15,000 to 2010 at about$32,500. The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 0 to 35,000 in intervals of 5,000." loading="lazy" decoding="async">

Find and interpret the y-intercept.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$15,000 to 2010 at about$32,500. The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 0 to 35,000 in intervals of 5,000." loading="lazy" decoding="async">

In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly.

• ⓐHow much did the population drop between the year 2004 and 2012?
• ⓑWhat is the average population decline per year?
• ⓒFind an equation for the population, P, of the school t years after 2004.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$15,000 to 2010 at about$32,500. The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 0 to 35,000 in intervals of 5,000." loading="lazy" decoding="async">

Draw a scatter plot for the data provided in (the referenced table). Then determine whether the data appears to be linearly related.

For the following exercises, use the graph in (the referenced figure), showing the profit, $y,$ in thousands of dollars, of a company in a given year, $x,$ where $x$ represents years since 1980.

$15,000 to 2010 at about$32,500. The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 0 to 35,000 in intervals of 5,000." loading="lazy" decoding="async">

Draw a best-fit line for the plotted data.

For the following exercises, use (the referenced table), which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year.

Year	2000	2002	2005	2007	2010
Percent Graduates	8.5	8.0	7.2	6.7	6.4

Determine whether the trend appears linear. If so, and assuming the trend continues, find a linear regression model to predict the percent of unemployed in a given year to three decimal places.

For the following exercises, use (the referenced table), which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year.

Year	2000	2002	2005	2007	2010
Percent Graduates	8.5	8.0	7.2	6.7	6.4

In what year will the percentage drop below 4%?

For the following exercises, use (the referenced table), which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year.

Year	2000	2002	2005	2007	2010
Percent Graduates	8.5	8.0	7.2	6.7	6.4

Based on the set of data given in (the referenced table), calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy.

For the following exercises, use the vertex $(h,k)$ and a point on the graph $(x,y)$ to find the general form of the equation of the quadratic function.

$(h,k)=(2,0),(x,y)=(4,4)$

For the following exercises, use the vertex $(h,k)$ and a point on the graph $(x,y)$ to find the general form of the equation of the quadratic function.

$(h,k)=(-2,-1),(x,y)=(-4,3)$