Download MAC 1105 – COLLEGE ALGEBRA Catalog Description: (3) (A.A.

MAC 1105 – COLLEGE ALGEBRA
Catalog Description: (3) (A.A.) Three hours lecture per week. Prerequisite: MAT 1033 or appropriate
score on the mathematics placement test. This course meets Area II requirements for both A.A. General
Education Requirements and A.S. General Education Requirements. This is a rigorous introduction to the
mathematical concepts necessary for successful study of MAC 1114, MAC 1140 or MAC 2233. This
course is primarily a conceptual study of functions and graphs, their applications, and of systems of
equations and inequalities. Linear, quadratic, rational, absolute value, radical, exponential and
logarithmic functions will be investigated. The use of a graphing calculator is integrated throughout this
course.
Performance Standards:
At the successful completion of this course, the student should be able to:
1. Use functions and function notation in modeling real-life phenomena.
2. Identify the domain and range for a given function using set builder notation, interval notation, or a
number line graph.
3. Determine if a given relation is a function by definition or by applying the vertical line test.
4. Use function notation as a name or as a range element corresponding to domain element.
5. Identify (x,f(x)) as an ordered pair on the graph of function f.
6. Evaluate a function given a table, graph, equation, or verbal description.
7. Find x and y intercepts given an equation or graph.
8. Sketch a graph of a function manually and on a calculator.
9. Determine the symmetry of a function from its equation and from its graph.
10. Determine whether a function is even or odd from its equation and from its graph.
11. Analyze linear, quadratic, cubic, square root, cube root, absolute value, and reciprocal functions.
12. Apply the graphical transformations of horizontal and vertical shifts, reflections about the y-axis and
x-axis, and stretching and compression to graph the above functions.
13. Determine intervals over which a function is increasing, decreasing, or constant.
14. Identify slope as the constant rate of change in the linear function.
15. Solve application problems involving linear functions.
16. Identify the vertex and axis of symmetry of a quadratic function.
17. Solve application problems involving quadratic functions including optimization.
18. Locate horizontal and vertical asymptotes of rational functions.
19. Classify basic exponential function as models of either exponential growth or exponential decay.
20. Determine the effect of a change in the base of an exponential function and of the coefficient.
21. Solve applied problems that are described by exponential functions.
22. Evaluate logarithms.
23. Use the properties of logarithms.
24. Solve exponential and logarithmic equations.
25. Solve equations and inequalities analytically and graphically.
26. Identify one-to-one functions graphically.
27. Find the inverse function of a given function.
28. Analyze the relationships between a function and its inverse.
29. Solve linear systems of equations and inequalities in two variables graphically, by the substitution
method, and by the elimination method.
30. Solve application problems using systems of equations.
31. Demonstrate proficiency with a graphing calculator as a support tool for problem solving.
32. Distinguish between exact answers and approximations.
33. Approximate the solutions to equations and inequalities graphically (using a graphing tool).
MAC 1105
2
MAC 1105 – COLLEGE ALGEBRA
Performance Standards Sample Questions
1.
Consider the function f (x) = x − 4 .
a.
Sketch the graph of the function by applying transformations to the graph of
g(x) = x .
b.
Identify the domain and range of the function using interval notation.
c.
Determine the intervals on which f (x) is increasing and decreasing, respectively.
d.
Determine the value(s) of x for which f (x) = 0.
e.
Locate the point (2, f (2)) on the graph.
f.
Determine f (-5).
g.
Discuss the symmetry of f (x).
h.
Determine whether f (x) has an inverse.
2.
The function f (x) = 0.4 x 2 − 36x + 1000 describes the number of accidents per 50 million
miles driven as a function of age x in years, where 16 ≤ x ≤ 74 .
a.
For what value of x does the function have a relative minimum?
b.
What is the minimum value of the function?
c.
Explain the meaning of your answers to (a) and (b) in the context of the problem.
3.
Determine whether the relation x 2 + y 2 = 4 represents a function.
4.
Use the vertex and intercepts to sketch the graph of the parabola:
5.
Determine whether the function g(x) = 3x 3 − 2x is even, odd, or neither.
6.
If f (x) = −3x 2 + 2 and g(x) = 3x − 5 , determine
f (−2) + g(3)
b.
f (g(x))
a.
c.
f (x) = −2x 2 − x + 5
f (g(2))
7.
In the year 2008, a company purchases an office machine for $9300. The machine is
expected to last for 6 years with a yearly loss in value of $1200. Write a linear equation
modeling V, the value of the machine, t years after 2008.
8.
Sketch the graph of g(x) = 3 + 2 x − 4 by applying transformations to the graph of
f (x) = x .
9.
Sketch the graph of f (x) =
10.
Write as a single logarithm: ln(x + 1) + 2ln(x + 2) − 3ln(x + 3)
11.
Suppose you have $7000 to invest. What investment yields a greater return over 5 years:
8.25% compounded quarterly, or 8.3% compounded semiannually?
3x −1
. Label the horizontal and vertical asymptotes.
x+2