options: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
problem_activity: Problem 1
A rectangular garden has a width of
$$x$$
feet. The length of the garden is
$$4$$
feet longer than the width. Around the garden there is a pathway that measures
$$3$$
feet across the path.
[IMG]
The expression below represents the area of the pathway, not including the garden.
$$(x+6)(x+10)-x(x+4)$$
Explain what each part of the expression represents in context of the situation.
a.
$$x$$
b.
$$x+4$$
c.
$$x+10$$
d.
$$x(x+4)$$
e.
$$(x+6)(x+10)$$
Problem 2
An artist has a strip of wood
$$8$$
feet long to make a large rectangular picture frame. The possible dimensions of the frame that the artist can create can be represented as
$$x$$
and
$$4-x$$
, as seen in the diagram below.
[IMG]
What is the largest area the artist can frame with the
$$8$$
feet of wood?


correct_option_index: 1