Graphing Function Relationships: Word Problems & Changes

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If you graph the total cost (y) against the miles driven (x), what does the slope of the graph represent?

• $0.20 per mile

• $50 flat fee

• $1.00 per mile

• $0.10 per mile

A gardener is planting flowers in a rectangular garden. The area of the garden is represented by the function A = l * w, where l is the length and w is the width. If the length increases while the width remains constant, how does the graph of the area change?

• The graph of the area increases linearly.

• The graph of the area decreases linearly.

• The graph of the area remains constant.

• The graph of the area increases exponentially.

A student tracks the number of hours studied (x) and the score received on a test (y). If the graph shows a linear relationship, what does the y-intercept represent in this context?

• The y-intercept represents the expected test score with zero hours studied.

• The y-intercept represents the minimum score achievable regardless of study hours.

• The y-intercept shows the average hours studied by students.

• The y-intercept indicates the maximum possible score on the test.

A local bakery sells cupcakes for $3 each and cookies for $2 each. If you graph the total cost (y) against the number of cupcakes (x), how would you represent the cost of cookies on the same graph?

• The cost of cookies can be represented as y = c + 2, where c is the number of cookies.

• The cost of cookies can be represented as y = 4c, where c is the number of cookies.

• The cost of cookies can be represented as y = 2c, where c is the number of cookies.

• The cost of cookies can be represented as y = 3c, where c is the number of cookies.

A bike rental service charges a one-time fee of $10 plus $5 per hour. If you were to graph the total cost against the number of hours rented, what does the point where the graph intersects the y-axis represent?

• The one-time fee of $10.

• The maximum rental time allowed.

• The cost per hour of rental.

• The total cost after one hour.

A school is tracking the number of students enrolled over the years. If the graph shows an increasing trend, what does this indicate about the function relationship over time?

• The function relationship indicates no change in enrollment over time.

• The function relationship shows a positive correlation over time.

• The function relationship suggests a random fluctuation in student numbers over time.

• The function relationship shows a negative correlation over time.

A fitness tracker records the number of calories burned (y) based on the time spent exercising (x). If the graph is a curve that flattens out, what does this suggest about the relationship between time and calories burned?

• The relationship shows that calories burned decreases as exercise time increases.

• The relationship indicates a linear increase in calories burned with time.

• The relationship suggests that more time always leads to more calories burned without limit.

• The relationship shows diminishing returns in calories burned with increased exercise time.

A store has a sale where the price of an item decreases by 10% each week. If you graph the price (y) against the number of weeks (x), what type of function does this represent?

• Exponential decay function

• Logarithmic function

• Quadratic function

• Linear function

A train travels at a constant speed of 60 miles per hour. If you graph the distance traveled (y) against time (x), what does the slope of the graph indicate?

• The slope represents the time taken for the journey.

• The slope indicates the speed of the train, which is 60 miles per hour.

• The slope indicates the total distance traveled by the train.

• The slope shows the acceleration of the train.

A water tank is being filled at a rate of 5 gallons per minute. If you graph the volume of water in the tank (y) against time (x), how would you describe the relationship shown in the graph?

• The relationship is constant.

• The relationship is linear.

• The relationship is quadratic.

• The relationship is exponential.