Understanding Functions and Their Properties

In the context of a mathematical function, which term is synonymous with "input values"?

• Range

• Dependent variable

• Domain

• Output values

For a function w(x) where w is the amount of water in a pool and x is the length of the pool, what does the independent variable represent?

• The amount of water in the pool.

• The length of the pool.

• The volume of the pool.

• The depth of the pool.

A function f is considered increasing on an interval if, for any two input values a and b in that interval where a < b, which of the following must be true?

• f(a) > f(b)

• f(a) = f(b)

• f(a) < f(b)

• f(a) >= f(b)

What are the input values called when a function's graph intersects the x-axis?

• Y-intercepts

• Ranges

• Zeros

• Domains

What is the term for the point on a function's graph where its concavity changes?

• Vertex

• Critical point

• Inflection point

• Turning point