Adrienne said that a vertical stretch by a factor of 4, a horizontal shift to the left 1 unit and a vertical shift down 3 units of the graph of the parent function f(x)=ex produce the graph of the function g(x)=4ex-1+3. Explain whether Adrienne is correct and if not determine the transformations that produce the graph of the function g(x)=4ex-1+3 from f(x)=ex.

Describe how the graph of y = −3f[2(x + 5)] − 4 can be obtained from the graph of f(x) = x3 . Be sure to fully describe the transformations.

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)

For each of the following functions, compare the graph of y = g(x) to the graph of f(x)=x3. Describe the transformation using words or a sketch. a. g(x)=3x3 b. g(x)=(3x)3 c. g(x)=(13x)3 d. Sometimes f(kx) will look like a vertical stretch. Explain why when you look at the graph of g(x) =(3x)3 it will appear to be stretched.