Answer and explanation:
To find : Describe the transformation(s) that take place on the parent function, \(f(x) =\log(x)\), to achieve the graph of \(g(x) = \log(-2x-4) +2\)
Solution :
Parent function: \(f(x) =\log(x)\)
Transformation function: \(g(x) = \log(-2x-4) +2\)
Re-write the transformed function by taking -2 common,
\(g(x) =\log(-2(x+2))+2\)
Step 1 - Shift 2 unit left i.e, f(x)→f(x+b) shifting left by b unit in parent function,
\(f(x)=\log(x+2)\)
Step 2 - Flip the graph about y-axis i.e, f(x)→ -f(x)
\(f(x)=\log[-(x+2)]\)
Step 3 - Stretch horizontally by factor 2 i.e, f(x)→f(bx) stretch horizontally by b unit
\(f(x)=\log[-2(x+2)]\)
Step 4 -
Shift vertically up by 2 units i.e, f(x)→f(x)+b shifting vertically by b unit
\(f(x) =\log(-2(x+2))+2=g(x)\)
In four steps the transformation is done.
