Question

which of the following best shows the values in the domain when the function is increasing?
between 3 and 9
between 0 and 6
between 3 and 6
between 6 and 9

Explanation:

Step1: Understand function increasing

A function is increasing when as \(x\) (domain) increases, \(y\) (range) also increases.

Step2: Analyze the table

Looking at the \(x\) (left - hand column) and \(y\) (right - hand column) values:

• For \(x = 5,y = 11\); for \(x=6,y = 12\). As \(x\) goes from \(5\) to \(6\) (within the range of \(x\) values in the table), \(y\) increases.
• For \(x = 6,y = 12\); for \(x = 7,y = 11\). Here \(y\) decreases as \(x\) increases.
• For \(x = 7,y = 11\); for \(x = 8,y = 8\). \(y\) decreases as \(x\) increases.
• For \(x = 8,y = 8\); for \(x = 9,y = 3\). \(y\) decreases as \(x\) increases.

The only interval where \(y\) (range) increases as \(x\) (domain) increases is when \(x\) is from \(5\) to \(6\) (a part of the interval between \(3\) and \(6\) if we assume the start of the relevant domain is \(3\) - since we have \(x = 5,6\) in the table and the options are given in ranges).

Answer:

between 3 and 6