## MTH 129 Chapter Objectives

### Chapter 1

1. Recognize a single-variable equation as linear and solve it (0, 1, or inf. many soln's).
2. Translate a problem situation into an equation and solve.
3. Write inequalities corresponding to problem situations.
4. Write an interval using inequalities and graph it.
5. Solve linear inequalities.
6. Solve application problems involving linear inequalities.
7. Solve absolute value equations.
8. Solve absolute value inequalities.
9. Identify and simplify complex numbers.
10. Add, subtract, multiply, and divide complex numbers.
11. Simplify powers of $i$.
12. Solve quadratic equations by factoring.
13. Solve quadratic equations by using square roots.
15. Determine the values of the variable that are restricted from a rational expression.
16. Solve rational equations that reduce to linear or quadratic.
17. Solve equations using odd roots.
19. Solve equations involving rational exponents.
20. Solve equations that are quadratic in form.

### Chapter 2

1. Graph two-variable equations in the rectangular coordinate system.
2. Find the distance between two points in the rectangular coordinate system.
3. Determine the midpoint of two points.
4. Use the standard form equation of a circle.
5. Graph circles.
6. Gain and demonstrate familiarity with some basic graphs.
7. Determine solutions of two-variable linear equations.
8. Graph a line by finding two points on the line.
9. Find the $x$- and $y$-intercepts of a line.
10. Compute the slope of a line and interpret it as a rate of change.
11. Identify equations of horizontal or vertical lines and graph them.
12. Determine lines parallel or perpendicular to given lines.
13. Find and apply the slope-intercept form of the equation of a line.
14. Find and apply the point-slope form of the equation of a line.
15. Graph a line using its slope and a point.
16. Find lines parallel or perpendicular to given lines.
17. Apply lines and linear equations in real-world applications.
18. Determine whether a relation is a function.
19. Determine the domain and range of a function.
20. Use function notation and evaluate functions.
21. Interpret graphs of functions.
22. Evaluate difference quotients.
23. Given the graph of a function, determine where the function is positive, negative, or zero.
24. Given the graph of a function, determine intervals on which the function is increasing, decreasing, or constant.
25. Given the graph of a function, determine the local maxima and minima.
26. Determine if a graph has symmetry.

### Chapter 3

1. Develop and demonstrate a familiarity with the graphs of basic functions (Toolbox Functions).
2. Apply the transformations (shifts, reflections, stretches, and compressions) to basic graphs to obtain more general graphs.
3. Determine the transformations that result in a given graph.
4. Develop a familiarity with the whole-number power functions and basic rational functions.
5. Apply transformations to basic functions.
6. Define and evaluate piecewise functions.
7. Sketch the graph of a piecewise-defined function.
8. Compute sums, differences, products, and quotients of functions.
9. Compute a composition of functions.
10. Write a function as a composition of functions.
11. Solve problems involving operations on functions.

### Chapter 4

1. Find the vertex, intercepts, and symmetry axis of a parabola.
2. Write a quadratic function in vertex form.
3. Find the equation of a quadratic function from its graph.
4. Solve application problems involving quadratic functions and parabolas.
5. Find the zeros of a polynomial and determine their multiplicities.
6. Carry out polynomial long division and synthetic division.
7. Apply the remainder and factor theorems.
8. Apply the Fundamental Theorem of Algebra.
9. Use common tests to determine the nature of a polynomial's zeros.
10. Factor a polynomial with real coefficients into a product of linear factors and irreducible quadratic factors.
11. Determine the end behavior of a polynomial function.
12. Use multiplicities of zeros and end behavior to graph a polynomial function.
13. Determine the domain of a rational function.
14. Determine the vertical, horizontal, and/or slant asymptotes of the graph of a rational function.
15. Sketch the graph of a rational function.
16. Solve polynomial inequalities.
17. Solve rational inequalities.

Last updated April 28, 2020

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