standard_description: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^(2) + y^(2))^(2) = (x^(2 )– y^(2))^(2) + (2xy)^(2 )can be used to generate Pythagorean triples.
problem_activity: Problem 1
The functions below are parent functions. Graph each one. Use either technology or a table of values where needed.
$${y=x}$$
$${y=x}^2$$
$${y=x}^3$$
$${y=|x|}$$
$${y=\sqrt{x}}$$
$${y=\sqrt[3]{x}}$$
Problem 2
Consider the two functions below.
$${{f(x)}=|x|}$$
$${{g(x)}=|x|+2}$$
Create a table of values for each function and use it to graph each function in the coordinate plane.
Looking at the tables and the graphs, what changed from the parent function,
$${f(x)}$$
, to the new function,
$${g(x)}$$
? What is the same?
Look at the corresponding work in the Desmos activity,
Introduction to Transformations of Functions
, slides 3–6.
Problem 3
Predict what the tables and graph would look like for each function below. Then refer to slide 7 in the Desmos activity,
Introduction to Transformations of Functions
, to try out other values for
$$k$$
.
$${y=|x|+5}$$
$${y=|x|-1}$$
$$y=|x|+k$$
A different parent function and transformations are shown below. Predict what each graph would look like. Then refer to slides 8–14 in the Desmos activity.
$${y=x^2}$$
$${y=x^2}+5$$
$${y=x^2}-1$$
$${y=x^2}+k$$


aligns: no