example 9\nselect the appropriate\nparent function (in blue) and\ntransform it to represent\nthe…

example 9\nselect the appropriate\nparent function (in blue) and\ntransform it to represent\nthe function:\n$f(x)=2\\sqrt3{x - 3}-2$

example 9\nselect the appropriate\nparent function (in blue) and\ntransform it to represent\nthe function:\n$f(x)=2\\sqrt3{x - 3}-2$

Answer

Explanation:

Step1: Identify Parent Function

The parent function for a cube root function is ( y = \sqrt[3]{x} ). This is the basic cube root function without any transformations.

Step2: Analyze Horizontal Shift

The function ( f(x) = 2\sqrt[3]{x - 3}-2 ) has a horizontal shift. The ( x - 3 ) inside the cube root means the parent function ( y=\sqrt[3]{x} ) is shifted 3 units to the right.

Step3: Analyze Vertical Stretch

The coefficient 2 in front of the cube root means the parent function is vertically stretched by a factor of 2.

Step4: Analyze Vertical Shift

The -2 at the end means the function is shifted 2 units down.

Step5: Graph Transformations

Start with the parent function ( y = \sqrt[3]{x} ) (blue). Shift it 3 units right, stretch vertically by 2, then shift 2 units down to get ( f(x)=2\sqrt[3]{x - 3}-2 ).

Answer:

The parent function is ( y = \sqrt[3]{x} ). Transform it by shifting 3 units right, vertically stretching by a factor of 2, and shifting 2 units down to represent ( f(x)=2\sqrt[3]{x - 3}-2 ).