The purpose of this Warm-up is for students to compare different ways to describe a transformation of a function . They complete missing entries in a table where a series of transformations are described using words, function notation, and an expression in terms of . Several of the transformations purposefully relate to one another in order for students to make connections, such as how a horizontal translation ends up "inside" the function since it affects the input, while a vertical translation is "outside" since it affects the output.

As students compare the representations of a function under a transformation, they look for and make use of structure (MP7).

Invite students to explain how they filled in the missing entries in the table. Here are some questions for discussion:

• “How did you decide which values go 'inside' the square root?” (Translating right 5 is something that affects the input of a function, so the +5 goes with the inside of the square root.)
• “How did you decide which values go 'outside' the square root?” (Translating down 3 units is something that affects the output of a function, so the -3 goes outside of the square root.)

An important takeaway here is for students to separate transformations that affect inputs and transformations that affect outputs when writing equations to describe a transformation. Writing equations in terms of for transformations is the focus of the following activity.

In this activity, students transform functions but do not initially have enough information to do so. To bridge the gap, they need to exchange questions and ideas.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

In this activity, students apply the ideas from the Warm-up to write a transformed quadratic function in vertex form. Monitor for students who reason via transformations and for those who use their prior knowledge of vertex form to identify the vertex of . Also monitor for students who wrote different but correct equations for and . For example, if someone used a coefficient other than 1.