Question

how many zeros are indicated by the values in the table that represent the graph of a continuous function?

Explanation:

Step1: Apply the Intermediate Value Theorem

The Intermediate Value Theorem states that if a function \(y = f(x)\) is continuous on an interval \([a,b]\) and \(k\) is a number between \(f(a)\) and \(f(b)\), then there exists at least one number \(c\) in \((a,b)\) such that \(f(c)=k\). For a zero, \(k = 0\).

• Between \(x=-2.4\) (\(y = 0.69\)) and \(x=-1.8\) (\(y=-0.39\)): Since \(y\) changes sign (from positive to negative), there is at least one zero in the interval \((-2.4,-1.8)\).
• At \(x = 0\), \(y=0\), so \(x = 0\) is a zero.
• Between \(x = 1.2\) (\(y=-0.24\)) and \(x = 1.8\) (\(y = 0.39\)): Since \(y\) changes sign (from negative to positive), there is at least one zero in the interval \((1.2,1.8)\).

Answer:

There are \(3\) zeros.