Question

Hi, can someone help me i’m stuck on all 3 questions

Answer 1

Please find attached the graphs of the relationship created with MS Excel

The type of relationships are;

1. f(x) = |x|; Function

2. f(x) = x - 3; Function

3. x = |x|; Function

The details of the evaluation of the relationship are as follows;

1. f(x) = |x|

`\begin{tabular} c \cline{1-2}x & f(x)\\ \cline{1-2}-4 & 4 \\\cline{1-2}-2 &2 \\\cline{1-2}0 &0\\\cline{1-2}2 & 2\\\cline{1-2}4 & 4 \\\cline{1-2}6 &6 \\\cline{1-2}\end{tabular}`

The above table indicates that each value of x has exactly one value of y hence the relationship is a function based on the definition of a function

Please find attached the graph of f(x) = |x|, created with MS Excel

The graph passes the vertical line test, therefore, the relationship is a function

2. f(x) = x - 3

`\begin{tabular} \cline{1-2}x & f(x)\\ \cline{1-2}-4 & -7 \\\cline{1-2}-2 &-5 \\\cline{1-2}0 &-3\\\cline{1-2}2 & -1\\\cline{1-2}4 & 1 \\\cline{1-2}6 &3 \\\cline{1-2}\end{tabular}`

The values in the table indicates that each value of x maps onto exactly one value of y hence the relationship is a function

Please find attached the graph of f(x) = x - 3, created with MS Excel

The graph passes the vertical line test therefore, the relationship is a function

3. x = |y|

`\begin{tabular} c \cline{1-2}x & y\\ \cline{1-2}2 & -2 \\\cline{1-2}1 &-1 \\\cline{1-2}0 &0\\\cline{1-2}1 & 1\\\cline{1-2}2 & 2 \\\cline{1-2}\end{tabular}`

The above table indicates that the value of x = 2, has two values of y, which are y = -2, and y = 2.

Similarly, the value of x = -1, has two values y, which are y = -1, and y = 1

Therefore, the relationship is not a function based on the definition of a function

Please find attached the graph of x = |y|, created with MS Excel

The graph does not pass the vertical line test, therefore, the relationship is not a function