Question

Think about the three representations of functions you learned above. Create a table, map, and graph of a function and a non-function

Answer 1

Certainly! Let's illustrate the differences between a function and a non-function using a table, a mapping diagram, and a graph.

### Function: \( f(x) = 2x + 3 \)

**1. Table Representation:**

| \( x \) | \( f(x) \) |
|---------|------------|
| 1 | 5 |
| 2 | 7 |
| 3 | 9 |
| 4 | 11 |

**2. Mapping Diagram:**

```
x f(x)
----------------
1 ----> 5
2 ----> 7
3 ----> 9
4 ----> 11

```

**3. Graph Representation:**

The graph of \( f(x) = 2x + 3 \) is a straight line with a slope of 2 and a y-intercept at \( (0, 3) \).


---

### Non-Function: \( g(x) = \sqrt{x} \) with the mapping \( (x, y) \)

**1. Table Representation:**

| \( x \) | \( y \) |
|---------|-----------|
| 0 | 0 |
| 1 | 1 |
| 4 | 2 |
| 4 | -2 | (This is the non-function aspect)

**2. Mapping Diagram:**

```
x y
----------------
0 ----> 0
1 ----> 1
4 ----> 2
|
----> -2 (This creates the non-function condition)

```

**3. Graph Representation:**

The graph of \( g(x) = \sqrt{x} \) is a curved line starting at the origin but since the square root function can produce multiple \( y \) values for a given \( x \) (like both 2 and -2 for \( 4 \)), it is represented as:


### Summary:

- The first example, \( f(x) = 2x + 3 \), is a function because each input \( x \) corresponds to exactly one output \( f(x) \).
- The second example with \( g(x) \) involves two outputs (2 and -2) for the input \( 4 \), making it a non-function.