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College Algebra Wrap-Up Week 2

Wrap-Up: Features of Functions

1) Select all functions that have the following properties:

Domain equal to

(−∞, ∞)

It is always

increasing

It is always bigger or

equal to 0, that is,

𝑓(𝑥) ≥ 0

It has a local or

absolute extreme

value

𝑓(𝑥) = 𝑥 ○ ○ ○ ○

𝑓(𝑥) = 𝑥3 ○ ○ ○ ○

𝑓(𝑥) = √𝑥 3

○ ○ ○ ○

𝑓(𝑥) = 1

𝑥2 ○ ○ ○ ○

𝑓(𝑥) = ln⁡(𝑥) ○ ○ ○ ○

𝑓(𝑥) = 𝑥2 ○ ○ ○ ○

𝑓(𝑥) = √𝑥 ○ ○ ○ ○

𝑓(𝑥) = 1

𝑥 ○ ○ ○ ○

𝑓(𝑥) = 𝑒𝑥 ○ ○ ○ ○

𝑓(𝑥) = |𝑥| ○ ○ ○ ○

2) Evaluate 𝑓(1) where 𝑓(𝑥) = ln(𝑥) and explain why your answer makes sense.

College Algebra Wrap-Up Week 2

3) Explain how you could determine which of the three graphs here is 𝑓(𝑥) = 3𝑥 using only the graph provided.

4) Explain how you could determine which of the three graphs here is 𝑔(𝑥) = log⁡(𝑥) using only the graph provided.