MAC 1105 Course and Unit Learning Outcomes

Here you can review the College Algebra general and unit-specific learning outcomes. You will be able to meet these learning outcomes by completing (satisfactorily) the weekly tasks specified on the course schedule.

Course Learning Outcomes

The student will be able to use processes, procedures, data, or evidence to solve problems and make effective decisions.

 Student will be able to read and comprehend data and information from a problem. Student will be able to recognize relevant data, translate data/information to a usable form and find algebraic models that describe the situation. Student will be able to analyze and apply appropriate strategies to find solutions to the problem. Student will be able to interpret the solutions and draw well supported conclusions.

The student will be able to use functions and functions concepts to analyze and model realistic situations.

 Student will be able to describe and analyze relationships between variable quantities in numerical, symbolic and graphical forms. Student will be able to apply function concepts such as domain and range, intercepts and inverse functions to realistic problems. Student will be able to use operations on and transformations of functions to analyze and apply each of the families of functions.

The student will be able to use appropriate technological tools to analyze and model realistic situations.

 Student will be able to use graphing calculators to graph functions. Student will be able to use graphing calculators to find functions that best model data sets. Student will be able to use graphing calculators to solve equations and inequalities.

Unit Learning Outcomes

After the successful completion of the corresponding units throughout the course, the student will be able to:

Unit 1

 Find the intercepts of a linear equation. Construct graphs of linear equations. Select appropriate viewing windows for graphs of linear functions Determine the slope of a line under various conditions. Determine the slope-intercept form of a linear equation given various data such as: slope and y-intercept, a coordinate and slope, two coordinates. Determine and apply the point-slope form and the standard form of a line. Determine the slope of a line under various conditions. Write equations of lines in slope-intercept form, point-slope form, and standard form. Find and interpret slope as rate of change in the context of a problem. Find and interpret the y-intercept in the context of a problem. Identify functions from verbal and algebraic descriptions, tables, and graphs. Identify and use function notation. Evaluate a function expressed verbally, numerically, and graphically. Identify properties of parallel and perpendicular lines. Determine whether two lines are parallel, perpendicular, or neither. Find equations of horizontal, vertical, parallel, and perpendicular lines,

and graph the corresponding lines.

 Determine the domain and range of a function algebraically. Recognize whether or not a given function is increasing, decreasing, or constant and model the behavior graphically. Retrieve information about a function from its graph: domain, range; increasing and decreasing intervals; output given an input and vice versa. Apply linear models to real world situations.

Unit 2

 Solve a system of linear equations graphically and through symbolic methods, including substitution and elimination. Recognize consistent, inconsistent, independent, and dependent system of equations. Apply systems of linear equations to real world situations. Solve linear inequalities in two variables. Apply linear inequalities to real world situations.

Unit 3

 Recognize basic functions and their graphs. Identify graphs as variations of basic functions. Graph various families of functions. Identify and find zeros of functions. Determine whether a given function is even, odd, or neither. Use transformations to graph a function. Determine the relative minima and relative maxima, absolute maximum and absolute minimum of functions. Find average rate of change. Calculate the difference quotient. Recognize and graph piecewise-defined functions. Apply non-linear models to real world situations.

Unit 4

 Solve quadratic equations by different methods: factoring, square root, quadratic formula, graphing. Given a quadratic equation, find the discriminant and state the nature of the solutions. Given a quadratic function, determine: concavity, vertex as maximum or minimum value, axis of symmetry, intercepts, width (narrow/wide); increasing and decreasing intervals. Graph parabolas. Find the equation of a parabola given the vertex and a second point, or given its graph. Find average rate of change. Solve quadratic inequalities by graphing. Apply quadratic models to real world situations.

Unit 5

 Determine whether a function is one-to-one. Make a table of values for a given function and its inverse. Given a function, find its inverse. Graph inverse functions. Perform basic operations on functions and find composite functions. Determine algebraically whether two given functions are inverses of each other.

Unit 7

 Recognize polynomial functions and their properties. Given a polynomial function: write it in descending order, find the degree, and identify the leading term and leading coefficient. Given a polynomial function, identify the zeros and corresponding multiplicity. Determine if a given binomial is a factor of a polynomial function. Determine the end behavior of polynomial functions Determine the intercepts of polynomial functions Determine the real zeros of polynomial functions and their multiplicities. Given the graph of a polynomial function, find: the number of turning points, zeros, whether the graph represents an odd or even degree function. Determine the equation of a polynomial function given its graph. Graph polynomial functions. Determine the domain of a rational function. Determine asymptotes of a rational function.

Unit 6

 Recognize and graph exponential functions. Find an exponential function given its graph. Given an exponential function, find: the initial value, growth or decay factor, and percent increase or decrease. Recognize and graph logarithmic functions. Evaluate logarithmic expressions. Recognize and apply properties of logarithms. Convert exponential equations to logarithmic form and vice versa. Find the inverse function of an exponential function; of a logarithmic function. Identify and apply natural exponential and logarithmic functions. Compute common and natural logarithms. Solve exponential and logarithmic equations. Apply the change of base formula. Apply exponential and logarithmic models to real world situations.

All Units:

 Use mathematical reasoning and common sense to evaluate answers and decide whether or not they are reasonable and logically support the conclusion. Perform all arithmetic operations using the graphing calculator. Use the graphing calculator to graph any given equation or function using an appropriate window. Demonstrate knowledge of a variety of graphing utility features.