FUNCTIONS (UNIVERSITY)

In this unit you will learn about Functions.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x².

In this unit you will learn about An algebraic expression is a string of numbers, variables, mathematical operations, and possibly exponents. For example, 4x + 3 is a basic algebraic expression. Or, we could get a little more complex with 3x(2x^2 + 2x – 5) + 6y. … In this case, the equation is a true number sentence when x = 1.

In this unit you will learn about A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in “width” or “steepness”, but they all have the same basic “U” shape.

This unit concentrates students’ attention on determining the values of the trigonometric ratios for angles less than 360° proving simple trigonometric identities and solving problems using the primary trigonometric ratios.

The sine law and the cosine law are developed. Students will learn to demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions while solving problems involving sinusoidal functions, including problems arising from real-world applications

In this unit, you will learn:

1. Periodic Functions and their Properties
2. Sinusoidal Functions – Sine and Cosine Functions
3. Transformations of Sinusoidal Functions
4. Graphing Combination of Transformations of Sine and Cosine Functions
5. Interpreting Sinusoidal Functions
6. Solving Problems Using Sinusoidal Functions

This unit will explore several topics including evaluating powers with rational exponents, simplifying expressions containing exponents, and describing properties of exponential functions represented in a variety of ways. The emphasis will be on modeling and problem solving using these concepts.

In this unit, students are introduced to a new type of function: the discrete function. In this course, discrete functions will take the form of sequences and series. A sequence is a list of numbers with some discernible pattern. Think back to your early studies of mathematics.

You may recall problems that would present you with a list of numbers and it was your job to determine the pattern and maybe even predict the next three terms in the sequence. This unit will involve building on students’ knowledge of sequences like these, but they will be modeling them using functions that allow them to predict any term in the sequence.

In this unit, students will connect and apply topics of study throughout the course to the concept of finance. The question every math teacher gets at least once per lesson is “when are we ever going to use this!?” The good news is this unit contains real-life applications of most concepts from this course! This unit will apply the knowledge students obtained from the following units: Algebraic Tools, Introduction to Functions and Exponential Functions.