함수 전체 문제

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

For the two linear functions, find the point of intersection: $\begin{array}{c}x=y+2 \\ 2x-3y=-1\end{array}.$

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

A car rental company offers two plans for renting a car.

Plan A: $25 per day and $0.10 per mile

Plan B: $40 per day with free unlimited mileage

How many miles would you need to drive for plan B to save you money?

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

Find the area of a triangle bounded by the y axis, the line $f(x)=12-4x,$ and the line perpendicular to $f$ that passes through the origin.

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

A town’s population increases at a constant rate. In 2010 the population was 65,000. By 2012 the population had increased to 90,000. Assuming this trend continues, predict the population in 2018.

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

The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold $C$ as a function of the year, $t.$ When will less than 6,000 people be afflicted?

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, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population (in hundreds) and the year over the ten-year span, (population, year) for specific recorded years:

$(4,500,2000);(4,700,2001);(5,200,2003);(5,800,2006)$

Use linear regression to determine a function y, where the year depends on the population. Round to three decimal places of accuracy.

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population (in hundreds) and the year over the ten-year span, (population, year) for specific recorded years:

$(4,500,2000);(4,700,2001);(5,200,2003);(5,800,2006)$

Predict when the population will hit 20,000.

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population (in hundreds) and the year over the ten-year span, (population, year) for specific recorded years:

$(4,500,2000);(4,700,2001);(5,200,2003);(5,800,2006)$

What is the correlation coefficient for this model?

Explain the advantage of writing a quadratic function in standard form.

How can the vertex of a parabola be used in solving real-world problems?