# g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function f.g(x)=frac{1}{3}(x-2)^{3}

g is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (c) Sketch the graph of g by hand. (d) Use function notation to write g in terms of the parent function f.$g\left(x\right)=\frac{1}{3}{\left(x-2\right)}^{3}$
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a) Parent function: $f\left(x\right)={x}^{3}$ b) Horizontal shift 2 units to the right Vertical shrink by a factor of $\frac{1}{3}$ c) The graph will be: d) In function notation, Answer: $g\left(x\right)=\frac{1}{3}f\left(x-2\right)$