Question

a graph is shown.
the graph of ( m(x) ) is transformed to produce the graph of ( h(x) ), such that ( h(x)=m(x - b)+k ). in this equation, the value of ( b ) is (langle) and the value of ( k ) is (langle).

Explanation:

Step1: Analyze horizontal shift

The graph of \(y = m(x - h)\) is a horizontal shift of \(y=m(x)\). If the graph of \(m(x)\) is shifted to the left by \(3\) units, then \(h=- 3\) (using the rule \(y = f(x - h)\), when \(h<0\) it's a left - shift).

Step2: Analyze vertical shift

The graph of \(y=m(x - h)+k\) is a vertical shift. The graph of \(m(x)\) is shifted down by \(4\) units. Using the rule \(y = f(x)+k\), when \(k < 0\) it's a downward shift, so \(k=-4\)

Answer:

\(h=-3\) and \(k = - 4\)