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

Here's the solution to the worksheet, with detailed explanations for each match.

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## Section A: Distance vs. Time Graphs

Graph A: Curved upward (concave up) — distance increases at an increasing rate → accelerating

Graph B: Straight line with positive slope — constant rate of change → constant speed

Graph C: Curved downward (concave down) — distance increases at a decreasing rate → decelerating/slowing down

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1) The distance travelled by a motorbike moving at a constant speed.
→ Constant speed means equal distance covered in equal time intervals → straight line graph.
✔ Answer: B

2) The distance travelled by a car accelerating.
→ Accelerating means speed is increasing → distance covered per unit time increases → curve gets steeper over time → concave up.
✔ Answer: A

3) The distance travelled by a cyclist who starts fast, but gradually slows down.
→ Starts fast → steep slope; slows down → slope becomes less steep → concave down curve.
✔ Answer: C

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## Section B: Various Real-Life Quantities vs. Time

Graph A: Starts flat (slow rise), then curves sharply upward → slow increase then rapid increase

Graph B: Starts flat, then curves upward → steady then rising

Graph C: Rises to a peak, then falls → increases then decreases

Graph D: Straight line with positive slope → steady, constant increase

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1) The birth rate was steady but now it is rising.
→ “Steady” = flat or slowly changing; “now rising” = slope increases → matches Graph B (starts flat, then rises).
✔ Answer: B

2) The price of gas has been rising steadily.
→ “Rising steadily” = constant rate of increase → straight line with positive slope.
✔ Answer: D

3) Unemployment rose slowly for 5 years, but now it is rising dramatically.
→ Slow rise → gentle slope; dramatic rise → steep slope → Graph A shows this transition.
✔ Answer: A

4) Inflation had been rising steadily but it is now falling.
→ Rising steadily → increasing; then falling → decrease → Graph C shows increase then decrease.
✔ Answer: C

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## Section C: More Real-Life Quantities vs. Time

Graph A: Straight line with negative slope → steady decrease

Graph B: Bell-shaped curve → rises to max, then falls (e.g., daily temperature)

Graph C: Straight line through origin with positive slope → proportional increase from zero

Graph D: Stepwise decrease → discrete drops (like tea being sipped)

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1) The number of Euros that can be purchased with £'s.
→ This depends on exchange rate. If the pound weakens against euro, you get fewer euros → steady decline. Graph A shows steady decrease.
*(Note: If the pound strengthens, euros increase — but context implies depreciation)*
✔ Answer: A

2) The price of housing has been falling steadily since 2011.
→ “Falling steadily” = constant decrease → straight line with negative slope.
✔ Answer: A

3) The temperature during the 24 hours of a summer’s day.
→ Typically: low in early morning, peaks around mid-afternoon, then falls at night → bell-shaped curve.
✔ Answer: B

4) The amount of tea in a cup that is being drunk.
→ Tea decreases as you drink it — likely in sips → stepwise drop (discrete decreases). Graph D shows this.
✔ 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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