MATH 25 - MIDYEAR 2025 - UNIT 1

1. A polynomial function is continuous at every number.

2. A rational function is continuous at every number in its domain.

3. A radical function is continuous at every number in its domain except on its boundary.

Continuity of Algebraic Functions

1. A polynomial function is continuous at every _______________.

2. A rational function is continuous at every _______________.

3. A radical function is continuous at every _______________.

• The domain is the set of all positive real numbers (0,∞).

What is the domain and the limits of a logarithmic function?

Sketch the graph.

• The domain is the set of all positive real numbers (0,∞).

What is the domain and the limits of a natural logarithmic function?

Sketch the graph.

• The domain is the set of all real numbers (-∞,∞).

What is the domain and the limits of an exponential function?

Sketch the graph.

• The domain is the set of all real numbers (-∞,∞).

What is the domain and the limits of an exponential function, e^x?

Sketch the graph.

Convert a logarithmic function to an exponential function.

Sketch the sin(x) function.

Sketch the cos(x) function.

A function f is continuous on

1. An open interval (a, b) if it is continuous at every number in (a, b).

2. A closed interval [a, b] if

   • It is continuous at every number in (a, b)

   • _______________ exists and is equal to _______________.

   • _______________ exists and is equal to _______________.

Give the step by step process of each type of problem.