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

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

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
Below is the graph and equation of the function
$$f$$
.
$$f(x)=(x-2)(x-5)\over(x-2)(x+1)$$
[IMG]
And below is the graph and equation of the function
$$g$$
.
$$g(x)={(x-5)\over(x+1)}$$
[IMG]
How are the functions
$$f$$
and
$$g$$
similar Different?
Problem 2
How are the functions
$${g(x)}$$
and
$${h(x)}$$
different? Similar?
$${g(x)}={x^2\over{x-2}}$$
$${h(x)}={x^2-4\over{(x-2)(x+3)}}$$


correct_option_index: 1