Applications of Functions: Interpreting Graphs Worksheet | PDF ... - Free Printable

Let’s solve each section step by step, matching the real-world scenarios to the correct graphs based on how the quantity (distance, rate, price, etc.) changes over time.

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## Section A: Distance vs. Time Graphs

Graphs:

- Graph A: Curve bending upward → increasing slope → accelerating
- Graph B: Straight line with constant positive slope → constant speed
- Graph C: Curve bending downward → decreasing slope → decelerating

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1) The distance travelled by a motorbike moving at a constant speed.

→ Constant speed = constant rate of change of distance → straight line
✔ Answer: B

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2) The distance travelled by a car accelerating.

→ Accelerating means speed is increasing → distance increases faster and faster → curve gets steeper → upward-bending curve
✔ Answer: A

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3) The distance travelled by a cyclist who starts fast, but gradually slows down.

→ Starts fast → steep slope → then slows → slope decreases → downward-bending curve
✔ Answer: C

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## Section B: Various Rates Over Time

Graphs:

- A: Starts flat (slow), then curves sharply up → slow start, then rapid increase
- B: Starts flat, then curves up → steady, then rising
- C: Rises to a peak, then falls → increases then decreases
- D: Straight line up → steady increase

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1) The birth rate was steady but now it is rising.

→ “Steady” = flat or very slow increase → “now rising” = slope increases → matches Graph B (starts flat, then curves up)
✔ Answer: B

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2) The price of gas has been rising steadily.

→ Steady rise = constant slope → straight line
✔ Answer: D

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3) Unemployment rose slowly for 5 years, but now it is rising dramatically.

→ Slow rise → shallow slope → dramatic rise → steep slope → matches Graph A (starts shallow, then steepens)
✔ Answer: A

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4) Inflation had been rising steadily but it is now falling.

→ Rising steadily → straight line up → then falling → slope becomes negative → matches Graph C (rises, peaks, then falls)
✔ Answer: C

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## Section C: Real-Life Quantities Over Time

Graphs:

- A: Straight line down → steady decrease
- B: Curve rises to a peak, then falls → like a day’s temperature
- C: Straight line up from origin → steady increase starting at zero
- D: Step-wise decline → sudden drops at intervals

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1) The number of Euros that can be purchased with £'s.

→ This depends on exchange rate. If the pound is weakening, you get fewer euros → steady decrease
✔ Answer: A

*(Note: This assumes the context implies the pound is losing value — common in such problems.)*

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2) The price of housing has been falling steadily since 2011.

→ Falling steadily = constant negative slope → straight line down
✔ Answer: A

*(Same as above — if graph A is used for steady decrease, it fits here too.)*

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3) The temperature during the 24 hours of a summer’s day.

→ Temperature rises during day, peaks in afternoon, then falls at night → bell-shaped curve
✔ Answer: B

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4) The amount of tea in a cup that is being drunk.

→ Starts full, then decreases — often in sips → step-wise decline (each sip removes some tea)
✔ Answer: D

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## ✔ Final Answers:

Section A:

1) B
2) A
3) C

Section B:

1) B
2) D
3) A
4) C

Section C:

1) A
2) A
3) B
4) D

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Let me know if you’d like visual explanations or sketches for any part!