options: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.  For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
problem_activity: Problem 1
Consider the three situations shown below.
$${|x|=5}$$
$${|x|<5}$$
$${|x|>5}$$
For each situation, let
$${{f(x)}=|x|}$$
and
$${{g(x)}=5}$$
. Graph each relationship between
$${f(x)}$$
and
$${g(x)}$$
in the coordinate plane and then use each graph to determine the solution to each situation.
Problem 2
Solve each absolute value inequality algebraically and verify the solution graphically.
a.
$${\left|x-{1\over2}\right|<3}$$
b.
$${\left|2x\right|>{7\over2}}$$
c.
$${\left|{1\over3}x\right|-4<-1}$$


correct_option_index: 1