Learning Outcomes for Math 1101

1.Demonstrate knowledge and understanding of the Math 1101 topics.

a. Students will determine whether a relation given as a set of points, a graph, or an equation represents a function.

b. Students will find the domain and range of a function.

c. Students will evaluate a function given by a graph or by an equation.

d. Students will combine functions arithmetically and relate combined functions to applications.

e. Students will form composite functions and specify their domains.

f. Students will determine whether or not a function has an inverse that is also a function.

g. Students will find the inverse of a function and state the domain and range of the inverse function.

h. Students will compute the slope of a line and interpret the slope as rate of change.

i. Students will recognize characteristics of linear, quadratic, piece-wise, third and fourth degree polynomial, exponential, and logarithmic functions.

j. Students will locate relative and absolute maxima and minima, and x- and y-intercepts of functions.

k. Students will solve equations involving linear, quadratic, piece-wise, third and fourth degree polynomial, exponential, and logarithmic expressions using algebraic and/or graphical methods.

l. Students will model real data using linear, quadratic, piece-wise, third polynomial, exponential, and logarithmic functions.

m. Students will solve systems of linear equations using the methods of elimination, substitution, and matrix inverses.

2. Formulate and solve problems from both mathematical and everyday situations.

a. Students will use combined functions including composite functions to solve problems.

b. Students will solve applied problems involving the various classes of functions described in 1i above.

c. Students will justify the appropriateness of selecting a particular class of function for modeling a set of data.

d. Students will discuss the advantages and disadvantages of using a model for interpolation and extrapolation.

e. Students will interpret and use properties such as relative and absolute maxima and minima and x- and y-intercepts in solving problems.

f. Students will solve problems using systems of equations.

3. Communicate mathematical ideas using both everyday and mathematical language.

a. Students will use function notation correctly.

b. Students will describe what the answer to a problem means in practical terms.

c. Students will express English statements using mathematical notation, and interpret symbolic mathematical statements in English.

4. Use calculator to explore and solve problems.

a. Students will graph a function on an appropriate viewing window using the graphing calculator.

b. Students will create regression models using the graphing calculator.

c. Students will use the Trace/Calc feature of the graphing calculator to solve equations and to locate relative maxima and minima as well as zeros of polynomial functions.

5. Participate in collaborative groups and cooperative learning.

a. Students will work collaboratively in small groups to solve problems.

6. Connect mathematics to other disciplines and real-world situations.

a. Students will model real data using mathematical functions.

b. Students will solve applied problems from a variety of disciplines.

7. Experience the power and usefulness of mathematics in solving real problems.

a. Students will learn mathematics in the context of solving real world problems.

b. Students will make decisions about real world problems based on the mathematical models that they have created.