Exploring Graph Intersections and Function Behavior

A graph shows the height of a plant over time. At what time does the plant reach its maximum height? What does this tell you about the growth rate?

• The plant's height continues to increase indefinitely.

• The plant reaches its maximum height at the start of the graph.

• The maximum height is reached at the lowest point of the graph.

• The plant reaches its maximum height at the peak of the graph.

Two lines on a graph represent the cost of two different phone plans. At what point do the costs become equal? What does this mean for choosing a plan?

• The costs are equal at the lowest point of the graph.

• The costs are equal at the highest point of the graph.

• The costs become equal at the intersection point of the two lines on the graph.

• The costs never become equal regardless of the plans.

A graph depicts the distance a car travels over time. What does the slope of the line indicate about the car's speed?

• The slope shows the car's fuel efficiency.

• The slope represents the car's acceleration.

• The slope indicates the car's direction of travel.

• The slope indicates the car's speed.

In a graph showing the temperature throughout the day, where do the lines intersect? What does this intersection represent in terms of temperature changes?

• The lines intersect at the highest temperature point.

• The lines intersect at the lowest temperature point.

• The lines intersect at the point where the temperatures are equal.

• The lines intersect at the beginning of the day.

A graph shows the number of visitors to a park over several months. What can you infer about the park's popularity during different seasons?

• The park has consistent visitor numbers year-round.

• Winter is the peak season for park visitors.

• Fall sees more visitors than spring and summer.

• The park is more popular in spring and summer than in fall and winter.

Two functions represent the profit and cost of a business. At what point do they intersect, and what does this point signify for the business?

• The intersection point signifies the break-even point for the business.

• The intersection point represents the total revenue of the business.

• The intersection point indicates the maximum profit for the business.

• The intersection point shows the point of highest cost for the business.

A graph illustrates the relationship between hours studied and test scores. How does the steepness of the line reflect the effectiveness of studying?

• A steeper line reflects a more effective studying method, leading to greater increases in test scores with additional study hours.

• A flat line shows that studying has no impact on test scores, regardless of hours spent.

• A steeper line means that studying is only effective for a limited number of hours before diminishing returns occur.

• A steeper line indicates less effective studying, resulting in lower test scores with more study hours.

In a graph showing the population of two cities over time, where do the lines cross? What does this crossing point indicate about the cities' growth?

• The lines cross at a point where one city is declining, showing a loss in population.

• The lines cross at the point of equal population, indicating a change in growth dynamics between the two cities.

• The lines cross at the point of maximum population, indicating a peak in growth.

• The lines cross at random intervals, indicating no significant change in growth patterns.

A graph displays the relationship between the amount of rainfall and crop yield. How can you determine the optimal rainfall for maximum yield from the graph?

• The optimal rainfall is at the peak of the yield curve on the graph.

• You can find the optimal rainfall by averaging all rainfall amounts on the graph.

• The optimal rainfall is at the lowest point of the yield curve.

• The optimal rainfall is determined by the total rainfall over the season.

A graph shows the relationship between speed and time for a runner. How can you interpret the runner's performance based on the graph's shape?

• The graph only shows the runner's distance covered.

• The runner's performance is determined solely by the time taken.

• The graph indicates the runner's age and experience level.

• The runner's performance can be interpreted by analyzing the graph's slope and shape, indicating speed consistency, acceleration, or fatigue.