math homework

Written Assignment #4 for MATH 111

Write careful, complete solutions for the following problems and submit them according to

Directions for Submitting Written Assignments, under Orientation to Online MATH 111 in the

Canvas classroom.

1. Given the two functions 2

( ) 4 1f x x x   and ( ) 1g t t 

a. Find and simplify   4gf .

b. Find and simplify   xfg .

c. Find and simplify    xgxf  .

2. Based on the graph of  xf shown here:

a. Sketch a graph of    12  xfxg

b. Find  21f .

c. Find   2ff .

3. Suppose the function P(t) gives the estimated population of a town t years after 2010. The

function N(c) gives the size of population that c police officers can patrol. Interpret (explain

in plain English) the meaning of the statement ))5((200 1

PN 

 .

4. Here is the graph of a function  xg . The graphs below are of transformations of  xg . Write the formula for each transformation. (Your formulas will include “  xg .”)

 xg :

Transformed graph a:

Transformed graph b:

Transformed graph c:

Transformed graph d: