Question

vi. describe the transformation of the function.
k(x) = 5h(x + 2) - 7

Explanation:

Step1: Analyze horizontal shift

The argument of \( h \) is \( x + 2 \), which means the graph of \( h(x) \) is shifted left by 2 units (since for a function \( h(x + c) \), \( c>0 \) shifts left).

Step2: Analyze vertical stretch/compression

The coefficient 5 in front of \( h(x + 2) \) means the graph is vertically stretched by a factor of 5 (since \( a>1 \) in \( ah(x) \) is a vertical stretch).

Step3: Analyze vertical shift

The \( - 7 \) at the end means the graph is shifted down by 7 units (since for \( h(x)+k \), \( k<0 \) shifts down).

Answer:

To obtain the graph of \( k(x) \) from the graph of \( h(x) \): first, shift the graph of \( h(x) \) 2 units to the left. Then, vertically stretch the resulting graph by a factor of 5. Finally, shift the graph 7 units down.