https://file.aiquickdraw.com/mathbot/file/1728395534393youb1w2b.jpg

The graph shows the number of gallons of water in a bathtub \( y \), as a function of time \( x \), where \( x \) represents time in minutes. The graph has a V-shape, which indicates that it follows an absolute value function.

Let’s analyze the key features:

1. At \( x = 0 \), \( y = 40 \) (starting with 40 gallons of water).
2. The graph decreases to \( y = 0 \) at \( x = 2.5 \) (the tub is empty at 2.5 minutes).
3. Then it increases again, and at \( x = 5 \), \( y = 40 \) (back to 40 gallons).

The V-shape is characteristic of an absolute value function, meaning the function is of the form \( y = |ax + b| + c \).

Looking at the choices:
- \( y = |16x - 40| \)
- \( y = |16x| - 2.5 \)
- \( y = |16x| + 2.5 \)
- \( y = |16x + 40| \)

Now, to find the best-fitting equation:

The function shifts vertically (up or down) based on the starting point of 40 gallons, and the rate of decrease and increase looks constant. Since the water is decreasing and increasing symmetrically and starts at 40, the equation should reflect that symmetry.

The best function here is \( y = |16x - 40| \), as it represents the correct behavior of the graph (sharp decrease and increase, centered at \( x = 2.5 \)).

Would you like further explanation or details?

Here are some related questions:
1. How does the absolute value function affect the shape of the graph?
2. What is the significance of the vertex in an absolute value function?
3. How can we determine the slope of the graph based on the rate of water change?
4. Why is the function centered around \( x = 2.5 \)?
5. What other transformations could affect this graph?

**Tip**: For an absolute value function, the vertex gives the point where the minimum or maximum occurs, and the graph reflects symmetrically around this point.

The graph shows the number of gallons of water in a bathtub, y, as a function of time, x. The options for the best-fitting function are: y = |16x - 40|, y = |16x| - 2.5, y = |16x| + 2.5, y = |16x + 40|.

Learn how to interpret and solve an absolute value function that models the number of gallons of water in a bathtub over time. This problem involves key algebraic concepts such as graphing and absolute value functions, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation