Section 15.6: Review for Chapter 15

Studying for a chapter examination is a personal process, one which nobody else can do for you. Simply take the time to review what you have done.

Here are the new terms in Chapter 15.

Abscissa [15.1]
Analytic geometry [15.1]
Axes [15.1]
Axis of a parabola [15.4]
Boundary [15.2]
Cartesian coordinate system [15.1]
Center of a circle [15.4]
Center of an ellipse [15.4]
Center of a hyperbola [15.4]
Circle [15.4]
Closed half-plane [15.2]
Conic sections [15.4]
Conjugate axis [15.4]
Constant function [15.5]
Coordinates [15.1]
Dependent variable [15.1]
Difference quotient [15.5]
Directrix [15.4]
Domain [15.5]
Eccentricity [15.4]
Ellipse [15.4]
Exponential curve [15.3]
Exponential function [15.5]
First component [15.
First-degree equation [15.1, 15.4]
Focus (pl. foci) [15.4]
Function [15.5]
Function machine [15.5]
Functional notation [15.5]
General form [15.4]
Graph [15.1, 15.3]
Half-plane [15.2]
Horizontal ellipse [15.4]
Horizontal hyperbola [15.1]
Horizontal line [15.1]
Hyperbola [15.4]
Independent variable [15.1]
Line [15.4]
Linear equation [15.1]
Linear function [15.5]
Logarithmic function [15.5]
Major axis [15.4]
Minor axis [15.4]
Open half-plane [15.2]
Ordinate [15.1]
Origin [15.1]
Parabola [15.3; 15.4]
Probability function [15.5]
Quadrant [15.1]
Quadratic function [15.5]
Range [15.5]
Satisfy [15.1]
Second-degree equation [15.4]
Slant asymptotes [15.4]
Slope [15.1]
Slope-intercept form [15.1]
Slope point [15.1]
Solution [15.1]
Standard form [1.3; 15.4]
Test point [15.2]
Transverse axis [15.4]
Vertex [15.3; 15.4]
Vertical ellipse [15.4]
Vertical hyperbola [15.4]
Vertical line [15.1]
Vertical line test [15.5]
x-intercept [15.1]
y-intercept [15.1]

If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).


Can you explain each of these important ideas in your own words?

Line (plotting points and slope-intercept) [15.1]
Vertical and horizontal lines [15.1]
Half-planes [15.2]
Equations by plotting points [15.3]
Parabolas [15.3]
Exponential curves [15.3]
Conic sections (general-form equation) [15.4]
Graph standard-form conic sections [15.4]
Functional notation [15.5]

Next, make sure you understand the types of problems in Chapter 15.


Graph lines by plotting points and by using the slope-intercept. [15.1]
Draw a line when given a point and the slope. [15.1]
Match a line with an equation. [15.1]
Solve applied problems involving lines, including future value, depreciation, profit, marginal
profit, cost, and marginal cost. [15.1]
Graph first-degree inequalities with two unknowns. [15.2]
Graph parabolas and exponential curves by plotting points. [15.3]
Solve applied problems involving exponential and parabolic models. [15.3]
Identify a conic section by looking at its equation. [15.4]
Sketch a conic section using its geometric definition. [15.4]
Sketch a conic section using its standard-form equation [15.4]
Solve applied problems involving the conic sections. [15.4]
Decide whether a given set is a function. [15.5]
Use the vertical line test to decide whether a given graph represents a functions. [15.5]
Determine the output value for a function. [15.5]
Evaluate functions. [15.5]
Graph a function and then classify it as a linear, quadratic, exponential, logarithmic, or
probability function. [15.5]
Find the difference quotient for a given function f. [15.5]

Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 15 Review Questions (whether they are assigned or not).

Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text. If you worked the problem correctly, move on to the next problem, but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.

We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination.