If f(x) = x + 4 and g(x) = 4x^2, find (f + g)(x) and (f + g)(2).

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. h(x)=√x−1+4

Describe the transformations and sketch the graphs of the following trigonometric functions. $$\begin{gathered} {\displaystyle a.f\left(x\right)=-2\cos \left(2x\right)+3} \\ b.g\left(x\right)=3\sin (x-\pi )-1 \end{gathered}$$

If $25,000 is invested for 15 years compounded quarterly and grows to $52,680. Find the interest rate to the nearest percent.

h is related to one of the parent functions described in this chapter. Describe the sequence of transformations from f to h.
$h(x)=|x+3|-5.$

Begin by graphing
${\displaystyle f\left(x\right)={\log }_{2}x}$
Then use transformations of this graph to graph the given function. What is the graphs

Sketch a graph of the function. Use transformations of functions whenever possible.
$f(x)=\{\begin{array}{lll}1-x& if& x<0\\ 1& if& x\ge 0\end{array}$