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 parent functions described in Section 1.6. Describe the sequence of transformations from f to g. g(x)

The graph below expresses a radical function that can be written in the form $f(x)=a(x+k{)}^{\frac{1}{n}}+c$. What does the graph tell you about the value of k in this function?

${\displaystyle (x+2)(x-\sqrt{3}i)(x+\sqrt{3}i)}$

Is the vector space $C\mathrm{\infty }[a,b]$ of infinitely differentiable functions on the interval [a,b], consider the derivate transformation D and the definite integral transformation I defined by $D(f)(x)=f\prime (x)D(f)(x)=f\prime (x)andI(f)(x)=\int xaf(t)dtf(t)dt$. (a) Compute $(DI)(f)=D(I(f))(DI)(f)=D(I(f))$. (b) Compute $(ID)(f)=I(D(f))(ID)(f)=I(D(f))$. (c) Do this transformations commute? That is to say, is it true that $(DI)(f)=(ID)(f)(DI)(f)=(ID)(f)$ for all vectors f in the space?

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. ${\displaystyle g\left(x\right)=\frac{1}{2}\mid x-2\mid -3}$

g is related to one of the parent functions. Describe the sequence of transformations from f to g. g(x) = -x^3 - 1

h is related to one of the six parent functions. (a) Identify the parent function f. (b) Describe the sequence of transformations from f to h. (c) Sketch the graph of h by hand. (d) Use function notation to write h in terms of the parent function f. ${\displaystyle h\left(x\right)=\mid 2x+8\mid -1}$