Checkpoint: Domain, Range, and End Behavior of Transformations Solution

Name the domain and range in set-builder notation. Then name the end behavior.

Square root

$a = 4, h = 1, k = - 3$

domain: $\{x | x \in ℝ, x \geq 1\}$

range: $\{y | y \in ℝ, y \geq - 3\}$

As $x \to + \infty, f (x) \to + \infty,$ and as $x \to 1, f (x) \to - 3$

Note

This graph is from the previous Checkpoint. In this Checkpoint, you should think about the effects a transformation has on the domain, range, and end behavior.

Q: What needs to be considered when determining the domain, range, and end behavior of a square root function?
A: The start/end point $(h, k) .$

Q: Why do you need this point?
A: Because it determines restrictions for the domain and range as well as the end behavior.