Question

1. Consider the functions ?(?) = √? + 1 , ?(?) = 2? 4−? , and ?(?) = ? 2 − 5

(a) Find ?(0), ?(0), ?(0)

(b) (??)(?)

(c) (? ∘ ?)(?)

(d) Find the domain of (? ∘ ?)(?)

(e) Find and simplify ?(?+ℎ)−?(?) ℎ .

(f) Determine if ? is an even function, odd function or neither. Show your work to justify your answer.

2. Sketch the piecewise function. ?(?) = { |? + 2|, ??? ? ≤ 0 √? + 2, ??? 0 < ? < 4 −(? − 5) 2 + 3, ??? ? ≥ 4

3. Consider 3? + 2 = 3?. Express ? in terms of ?.

4. Consider ?(?) = 3? 3 − 4. Find the inverse of ?. (? is a one to one function).

5. Identify the toolkit function, the shift, and sketch the graph. (a) ?(?) = 1 ?+1 (b) ?(?) = ? 3 + 2

Answer 1