Lesson 4.6 Worksheet Interpreting Graphs of Functions - Textbook ... - Free Printable

Let’s solve each problem step by step, interpreting the graphs based on the descriptions.

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Problem 1: Tyler went jogging after school. He started at a quick pace and then slowed down over time, but continued to always travel away from his home.

#### a. Which graph best represents Tyler’s distance from home over time?

We are looking for a graph where:
- Distance from home increases over time (since he’s always traveling away).
- The rate of increase slows down — meaning the slope of the distance-time graph gets less steep over time.

Let’s analyze the options:

- A: Straight line → constant speed → not slowing down → ✘
- B: Curve that starts steep and flattens out → distance increases, but slower and slower → ✔ This matches “started at a quick pace and slowed down.”
- C: Curve that gets steeper → speeding up → ✘

✔ Answer: B

> *Reasoning: Since Tyler is always moving away from home, distance must continuously increase. Because he slows down over time, the rate of increase (slope) must decrease — which is shown by a curve that flattens as time goes on.*

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#### b. Which graph best represents Tyler’s speed over time?

We need a graph showing:
- Speed starts high and decreases over time (he slows down).

Options:

- A: Speed increases then decreases → not consistent with “slowed down over time” → ✘
- B: Speed increases → opposite of what’s described → ✘
- C: Speed starts high and gradually decreases → ✔ Matches “started at a quick pace and slowed down.”

✔ Answer: C

> *Reasoning: Speed is decreasing over time, so the graph should show a downward trend. Graph C shows a smooth decrease in speed, which matches Tyler slowing down while still moving forward.*

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Problem 2: Caroline climbs a hill next to her house at a steady pace and then runs down.

#### a. Which graph best represents Caroline’s distance from home over time?

Key points:
- She climbs away from home → distance increases.
- Then she runs down → returns home → distance decreases back to zero.
- Climbing at a steady pace → straight line with constant slope.
- Running down → likely faster → steeper slope downward.

Options:

- A: Triangle shape — straight up, straight down → matches steady climb, then descent → ✔
- B: Curved hill shape — implies changing speed during ascent/descent → not “steady pace” → ✘
- C: Flat top → implies she stopped at the top → not mentioned → ✘

✔ Answer: A

> *Reasoning: Distance increases linearly (steady pace uphill), then decreases linearly (running down). Since running is typically faster than climbing, the downward slope may be steeper — which is shown in graph A.*

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#### b. Which graph best represents Caroline’s speed over time?

She:
- Climbs at a steady pace → constant speed (horizontal line).
- Then runs down → higher speed → another horizontal line at a higher level.

Options:

- A: Two horizontal lines — first lower (climbing), then higher (running down) → ✔ Perfect match.
- B: Starts at zero, increases, then levels off → implies accelerating to steady pace → not described → ✘
- C: Curved — changing speed → not “steady pace” → ✘

✔ Answer: A

> *Reasoning: “Steady pace” means constant speed. When she runs down, it’s implied she moves faster, so speed jumps to a higher constant value. Graph A shows two plateaus — first lower, then higher — matching this behavior.*

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Problem 3: Latrelle climbed to the top of a play structure, sat at the top for a while and then jumped down. Which graph best represents Latrelle’s distance from the ground over time?

Key events:
1. Climbs up → distance from ground increases.
2. Sits at top → distance stays constant (flat line).
3. Jumps down → distance rapidly decreases to zero.

Options:

- A: Curved climb, flat top, curved drop → climbing/jumping might not be linear, but “jumped down” suggests rapid drop — could be steep, but not necessarily curved → possible, but let’s check others.
- B: Straight up, straight down, no flat part → doesn’t show sitting at top → ✘
- C: Straight up, flat top, straight down → matches all three phases perfectly → ✔

✔ Answer: C

> *Reasoning: “Climbed” can be approximated as constant speed (straight line up), “sat for a while” = flat line, “jumped down” = rapid descent (straight line down). Graph C clearly shows these three distinct phases.*

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## ✔ Final Answers:

1a. B
1b. C
2a. A
2b. A
3. C

Let me know if you’d like visual annotations or further explanation!