The points H = (3,7); J = (0,4); K = (-1,8) and M = (-3,-4) can either be a relation or a function
- The domain is: [-3,-1,0,3]
- The range is: [-4,4,7,8]
- The ordered pair is a function
- The range of the table is [tex]y \ge 0[/tex]
The graph of the points
The points are given as:
H = (3,7); J = (0,4); K = (-1,8) and M = (-3,-4)
See attachment for the graph of the points
The domain of the points
This is the set of the x coordinates of the points
Hence, the domain is: [-3,-1,0,3]
The range of the points
This is the set of the y coordinates of the points
Hence, the range is: [-4,4,7,8]
How to determine if the ordered pair is a function
Recall that the points are:
H = (3,7); J = (0,4); K = (-1,8) and M = (-3,-4)
Rewrite the points using mapping
[tex]\left[\begin{array}{c}3&0&-1&-3\end{array}\right] \to \left[\begin{array}{c}7&4&8&-4\end{array}\right][/tex]
None of the x values point to multiple y values.
Hence, the ordered pair is a function
How to complete the table
The function is given as:
[tex]f(x) = x^2[/tex]
When x = -1, we have:
[tex]y = (-1)^2 =1[/tex]
For other values, we have:
[tex]y = (0)^2 =0[/tex]
[tex]y = 1^2 =1[/tex]
[tex]y = 2^2 =4[/tex]
Hence, the complete table is:
[tex]\left[\begin{array}{ccc}x&f(x) = x^2&f(x)\\-1&y= (-1)^2&1\\0&y= 0^2&0&1&y= 1^2&1&2&y= 2^2&4\end{array}\right][/tex]
Hence, the range of the function is [tex]y \ge 0[/tex]
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