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 \( (0, 3) \).

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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.