https://file.aiquickdraw.com/mathbot/file/1727691799051fnqd9nva.jpg

Let's break down the problem you're working on and review your steps.

### The given function:
\[ y = \sqrt[3]{x} + 2 \]

You were tasked with filling out the table, plotting points, and determining if this is a function.

### Table Check:
In your table, the values of \( x \) and \( y \) are:
- \( x = 0 \), \( y = \sqrt[3]{0} + 2 = 0 + 2 = 2 \)
- \( x = -1 \), \( y = \sqrt[3]{-1} + 2 = -1 + 2 = 1 \)
- \( x = -2 \), \( y = \sqrt[3]{-2} + 2 = \sqrt[3]{-2} + 2 \approx 0.37 \) (not 0)
- \( x = -3 \), \( y = \sqrt[3]{-3} + 2 \approx 0.88 \)
- \( x = -4 \), \( y = \sqrt[3]{-4} + 2 \approx 0.39 \)

It seems that the value \( y = 0 \) for \( x = -2 \) might be incorrect based on the function. The value should be approximately 0.37.

### Is this a function?
Yes, this is a function because for each input \( x \), there is exactly one output \( y \). The cube root function, \( \sqrt[3]{x} \), is continuous and well-defined for all real values of \( x \), and adding 2 ensures there is only one value of \( y \) for each \( x \).

Would you like further details on plotting this function or any questions about graphing or calculating values?

### 5 Questions to expand:
1. How would the graph of \( y = \sqrt[3]{x} + 2 \) look based on the table values?
2. How does the cube root function differ from a square root function in terms of graphing?
3. Can you find additional values for \( x \) and \( y \) to refine the graph more accurately?
4. What happens to \( y \) as \( x \) becomes more negative in the cube root function?
5. How do you verify if a relation is a function using the vertical line test?

#### Tip:
When checking if a relation is a function, ensure that every input \( x \) has only one corresponding output \( y \). You can use tools like the vertical line test on a graph.

Explore whether the relation y = √[3]{x} + 2 is a function by analyzing the table of values and graph. The cube root function is continuous and well-defined, ensuring a unique output for each input. Suitable for high school students learning about functions and graphing.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation