# Freshman Math Program

## Math 110 Learning Objectives

__110-1 Concept of Function__

Students will be able to…

- Identify if a relationship is a function and justify with the definition of a function.
- Demonstrate proper use of function notation.
- Given any of the four representations of a function, (algebraic, table, graph, contextual), students will be able to …
- Identify independent and dependent variables.
- Identify domain and range using interval or inequality notation.

**for all functions not listed in 110-2

__110-2 Families of Functions__

Students will be able to identify, solve for, and/or interpret the characteristics of each family of functions as appropriate (linear(L), exponential(E), logarithmic(G), power(P), polynomial(Y), quadratic(Q)):

- Intercepts
- Rates of Change
- Asymptotes
- End Behavior
- Domain and Range (using interval or inequality notation).
- Maximum and Minimum

Given any of the four representations of a function, students will be able to …

- Identify the function family
- Match to an equivalent representation
- Create an equivalent representation

Students will be able to write the equation for

- A linear function (from the vertical intercept and a rate OR from two points)
- A piecewise function (from a table, graph or context)
- An exponential function (from the vertical intercept and a rate, from the vertical intercept and another point, or from financial information)
- A power function (from context)

Given any of the four representation of a function, students will be able to identify and apply simple transformations:

- Horizontal/vertical shifts
- Horizontal/vertical axis reflections

__110-3 Modeling with technology__

Given data, students will be able to …

- Identify the most appropriate model based both on technology and the context of the situation and justify reasoning.
- Use technology (regression) to find a curve of best fit.

__110-4 Algebraic Manipulation__

Students will be able to perform the following manipulative skills and interpret the results:

- Given input, find output.
- Given output, find input.
- Students will be able to perform the following manipulative skills with algebraic expressions and equations:
- Use the rules of integer and rational exponents to simplify simple expressions.
- Rewrite a logarithmic equation into exponential form and vice versa.
- Factor simple equations.

__110-5 Systems__

Given a system of linear equations…

- Write equations for the system (in standard or slope-intercept form).
- Solve and interpret the results of a system of equations both graphically and algebraically.

Given a system of inequalities…

- Write the system of inequalities.
- Solve the system graphically.

__110-6 Composition and Inverses__

- Perform a composition of two functions both with specific numbers and with variables.
- Find the inverse of a given function using proper inverse function notation.
- Given a context and a function such as t-1(4)=20, a student will be able to interpret the equation in context.

__110-7 General Mathematical Skills__

- Explain complex mathematical concepts and procedures using appropriate mathematical terminology.
- Organize and update a math portfolio as directed in a portfolio.