Here are the solutions for the problems on the worksheet.
Example 1: Tony’s Books
1. What is the zero of this function? What does it represent in the context of the problem?
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Zero: The zero is at
0. (This is where the graph starts at the origin).
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Context: It represents that at day 0 (before he started counting or reading), Tony had read
0 books.
2. What is the domain? What does it represent in this context?
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Domain: The domain is
$x \ge 0$ (all numbers greater than or equal to 0).
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Context: This represents
time. Since time cannot go backwards, it starts at 0 days and continues forward forever.
3. What is the range? What does it represent in this context?
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Range: The range is
$y \ge 0$ (all numbers greater than or equal to 0).
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Context: This represents the
number of books. You cannot read a negative amount of books, so the count starts at 0 and goes up as he reads more.
4. What is the interval of increase? What does it represent in this context?
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Interval: The interval of increase is
$(0, \infty)$ (from 0 to infinity).
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Context: This means that as time goes on, the total number of books Tony has read
keeps going up. He never stops adding to his total count.
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Example 2: Jill’s Ball
1. What is the zero of this function? What does it represent in the context of the problem?
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Zero: Looking at the grid, the ball hits the ground (height = 0) at
3 seconds. So, the zero is
3.
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Context: It represents the moment the ball
hits the ground. After 3 seconds, the ball is no longer in the air.
2. What is the domain? What does it represent in this context?
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Domain: The domain is
$0 \le x \le 3$ (from 0 to 3).
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Context: This represents the
time the ball was in the air. The event started at 0 seconds and ended when the ball landed at 3 seconds.
3. What is the range? What does it represent in this context?
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Range: The ball started at a height of 2 feet and went up to a peak of 3 feet before falling. So, the range is
$0 \le y \le 3$.
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Context: This represents the
height of the ball. The lowest it got was 0 feet (ground) and the highest it got was 3 feet.
4. What is the interval of decrease? What does it represent in this context?
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Interval: The ball goes up until $x = 1$, then it comes down. So, the interval of decrease is
$(1, 3)$.
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Context: This represents the part of the flight where the ball is
falling down towards the ground. This happens between 1 second and 3 seconds.
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Final Answer:
Example 1 Answers:
1. Zero:
0; Represents:
0 books read at the start.
2. Domain:
$x \ge 0$; Represents:
Time starting from day 0.
3. Range:
$y \ge 0$; Represents:
The count of books cannot be negative.
4. Interval of Increase:
$(0, \infty)$; Represents:
The total number of books keeps growing over time.
Example 2 Answers:
1. Zero:
3; Represents:
The ball hits the ground after 3 seconds.
2. Domain:
$0 \le x \le 3$; Represents:
The duration of the toss from start to landing.
3. Range:
$0 \le y \le 3$; Represents:
The height varies between the ground (0) and the peak (3).
4. Interval of Decrease:
$(1, 3)$; Represents:
The time period when the ball is falling down.
Parent Tip: Review the logic above to help your child master the concept of functions and graphs worksheet.
