For Water World’s tube rentals, the profit function D = n(54 − n) − 10n is graphed as a downward-opening curve. Which statement best describes what the increasing-then-decreasing behavior means for daily profit?

Profit increases as more tubes are rented up to a certain number, then decreases if even more tubes are rented.

Profit is constant no matter how many tubes are rented.

Profit decreases at first, then increases without bound.

Profit alternates between increases and decreases every few rentals.

A newspaper graph titled “Landfill Area Remaining 2000–2005” shows the area (square kilometers) remaining each year from 2000 to 2005, with a slight downward trend. Which description best matches the behavior of the function over these years?

The area decreases overall, with small declines from year to year.

The area increases steadily each year.

The area stays exactly the same each year.

The area first increases sharply, then drops to zero.

Is the relation a function? Explain. Use the input–output table shown to decide whether each input maps to exactly one output. Input Output 6 4 -2 -3 9 -9 -6 -3

Yes, every input has exactly one output.

No, an input repeats with two different outputs.

No, because there are negative numbers.

Yes, because the outputs are all different.

Is the relation a function? Explain. Consider the set of ordered pairs {(2, 15), (15, -4), (-9, -7), (13, 14)}.

Yes, each x-value appears once.

No, some x-values repeat with different y-values.

No, because a y-value is negative.

Yes, because the y-values are all unique.

Is the relation a function? Explain. Consider the set of ordered pairs {(-1, 3), (-2, 8), (3, 10), (-2, 6)}.

No, the input -2 maps to two different outputs.

Yes, each input has one output.

Yes, because there are four ordered pairs.

Is the relation a function? Explain. Use the input–output table shown to decide whether each input maps to exactly one output. Input Output 8 -1 9 -8 -6 -7 8 -6 7 -2

No, input 8 has two different outputs.

Yes, every input has exactly one output.

No, because some outputs are negative.

Yes, because the table has five rows.

Ayesha is a gardener who makes square gardens in various sizes. The table shows the side lengths, in feet, and the areas of various gardens, in square feet. Side Length (feet) Area (square feet) 14 196 18 324 22 484 26 676 30 900 Write the values from the table as a set of ordered pairs (side length, area). Which option lists the correct set?

{(14, 196), (18, 324), (22, 484), (26, 676), (30, 900)}

{(196, 14), (324, 18), (484, 22), (676, 26), (900, 30)}

{(14, 14), (18, 18), (22, 22), (26, 26), (30, 30)}

{(14, 196), (18, 324), (22, 676), (26, 484), (30, 900)}

Using the same table of side lengths and areas for Ayesha’s square gardens, decide whether the relation from side length to area is a function.

Yes, each side length corresponds to exactly one area.

No, some side lengths have two different areas.

No, because areas are large numbers.

Yes, because the table has five entries.

Tamar has her own business repairing computers. The set of ordered pairs below represents various hours worked and her charge. For example, (1, 45) means 1 hour worked and a $45 charge. {(1, 45), (2, 90), (5, 225), (8, 360)} Explain what the ordered pair (5, 225) represents.

5 hours worked and a $225 charge

225 hours worked and a $5 charge

5 computers repaired and a $225 tip

Using the ordered pairs {(1, 45), (2, 90), (5, 225), (8, 360)}, decide whether the relation from hours worked to charge is a function.

Yes, each number of hours corresponds to exactly one charge.

No, some hours have two different charges.

No, because the charges increase.

Yes, because there are four ordered pairs.

A hiker climbs up a steep bank and then rests for a minute. He then walks up a small hill and finally across a flat plateau. Which sketch of an elevation–time graph matches this description? Option a shows elevation increasing steeply, then a short flat segment, then a gentle increase, then a flat segment. Option b shows elevation increasing and then a long flat segment. Option c shows elevation increasing, a short flat segment, then increasing again and ending still rising. Option d says any of the graphs could represent the situation, depending on the hiker’s speed.

Graph a: steep rise, flat, gentle rise, flat

Graph c: rise, short flat, rise, ending still rising

Any of the graphs could represent the situation, depending on the hiker’s speed

Which speed–time graph below matches this situation? A car traveling at 0 mi/h accelerates to 25 mi/h over the first 5 seconds, maintains that speed for the next 5 seconds, and then accelerates to 48 mi/h during the next 5 seconds.

Graph a: speed rises to 25 mi/h by 5 s, stays at 25 mi/h until 10 s, then rises to 48 mi/h by 15 s

Graph b: speed rises steadily to 50 mi/h by about 12 s, then remains at 50 mi/h

Graph c: speed decreases to 25 mi/h by 6–7 s, stays constant, then decreases to near 0 by 14–15 s

Graph d: speed rises to about 50 mi/h by 6 s, stays near 50 mi/h until 10 s, then drops to near 0 by 14–15 s

Jeff writes the equation $$y=-108x+3240$$ for the amount he owes after x payments. A graph shows how much Ella owes after each payment. Whose furniture costs more?

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Topic 3: Use Functions to Model Relationships - Revision

Authored by Samo Youssef

Mathematics

6th Grade

Topic 3: Use Functions to Model Relationships - Revision

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Function A

Function B

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Function B

Function A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Graph the ordered pairs from the table. Determine if the relation is a function. Table: ordered pairs (−3, −4), (0, 5), (1, −5), (3, 1).

The relation is a function.

The relation is not a function.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Graph the ordered pairs from the table. Determine if the relation is a function. Table: ordered pairs (−1, 3), (1, −1), (2, 2), (1, 3).

The relation is a function.

The relation is not a function.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Determine which graph represents a function.

Graph a: a sideways curved graph (opening to the right) that fails the vertical line test.

Graph b: an oval (ellipse) centered near the origin that fails the vertical line test.

Graph c: several separate plotted points with no repeated x-values that pass the vertical line test.

Graph d: an upward-opening parabola that passes the vertical line test.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The graph shows the height of a hiker above sea level. The hiker walks at a constant speed for the entire trip. Describe the behavior of the function in each interval (1) through (5).

The function is increasing in intervals 1, 3, and 4. The function is decreasing in interval 5. The function is constant in interval 2.

The function is increasing in intervals 1 and 3. The function is decreasing in interval 5. The function is constant in intervals 2 and 4.

The function is increasing in intervals 1 and 3. The function is decreasing in intervals 4 and 5. The function is constant in interval 2.

The function is increasing in intervals 1, 2 and 3. The function is decreasing in interval 5. The function is constant in interval 4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Select a graph for the situation. You wait for the express bus for 30 minutes, get on and ride the bus non-stop for 3 miles, and then walk another mile to your home. Choose the graph of distance (mi) versus time (min) that shows distance staying at 0 for 30 minutes, then a steep increase to 3 miles, followed by a slower increase to 4 miles.

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Topic 3: Use Functions to Model Relationships - Revision

Graph the ordered pairs from the table. Determine if the relation is a function. Table: ordered pairs (−3, −4), (0, 5), (1, −5), (3, 1).

Graph the ordered pairs from the table. Determine if the relation is a function. Table: ordered pairs (−1, 3), (1, −1), (2, 2), (1, 3).

Determine which graph represents a function.

The graph shows the height of a hiker above sea level. The hiker walks at a constant speed for the entire trip. Describe the behavior of the function in each interval (1) through (5).

A hiker climbs up a steep bank and then rests for a minute. He then walks up a small hill and finally across a flat plateau. Which sketch of elevation versus time matches this description?

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