Describe the transformations that must be applied to y=x^2 to create the graph of each of the following functions. a) y=1/4(x-3)^2+9b) y=((1/2)x)^2-7

Sketch a graph of the function. Use transformations of functions when ever possible. ${\displaystyle f\left(x\right)=1+\sqrt{x}}$

A wheel with a 30-cm radius is rotating at a rate of 3 radians/sec. What is the linear speed of a point on its rim, in meters per minute?

Graph f and g in the same rectangular coordinate system. Use transformations of the graph off to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range.
${\displaystyle f\left(x\right)=\ln x\text{and}g⟨x)=-\ln \left(2x\right)}$

An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as time goes on. Tell which of the following observational studies are retrospective and which are prospective. Out of curiosity, Mimi looks up the ages of all the Best Actress winners in the years they won their Oscars, and then gathers the same data for the Best Actor winners, to sec whether male or female winners were, on the average younger

Let L(Rm,Rn) be the set of all linear transformations from Rm to Rn. Is L(Rm,Rn), a subspace of F(Rm,Rn), the space of all functions from Rm to Rn? Justify your answer carefully.

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)

Given that f(x) = 3x - 7 and that (f + g)(x) = 7x + 3, find g(x).