Revised SP08

Review Sheet for Exam 1

Modeling Algebra

Important Topics to know:

Sec 1.1 - / Functions, Vertical Line Test, independent and dependent variables
pp. 19-25 #1,2, 8,12, 17,21, 34, 45, 49
Sec 1.2 - / Plotting points, viewing a complete graph, scatter plots
pp. 36-40 #1-5 odd, 21, 27-30, 41, 43, 45
Sec 1.3 - / Identifying a linear function, x-intercepts, y-intercepts, slope, constant rate of change
pp. 51 – 55 #1-17 odd, 31, 34, 36, 43, 47, 51, 52, 54
Sec 1.4 - / Equation of a line, slope-intercept form, average rate of change, slopes of vertical and horizontal lines
pp. 63-69 # 6, 9, 16, 18, 37, 38, 43, 51, 53, 63
Sec 1.5 - / Algebraic solutions, graphical solutions, finding zeros, solving using real world data
pp. 78 -81 # 1-12, 39, 44, 45, 49, 58
Sec 1.6 - / Fitting lines to real-world data points using linear regression, finding “best fit” line
pp. 94-101 # 1-8, 19, 21, 24, 29, 36, 41
Lab - / Describing the graph indicating vertical intercept, rate of speed, direction and time interval.

Formulas and Concepts:

  • Independent variables are represented on the horizontal axis. Dependent variables are represented on the vertical axis.
  • Graphs of data can be non-linear, approximately linear, or linear. We can determine this by looking at the graph, the table of values and/or the function.
  • X-intercepts are found when we set y = 0.
  • Y-intercepts are found when we set x = 0.
  • Slope of a line measures steepness and direction. It is defined as
  • Slope-intercept form of a line is, where m is defined as the slope and b is the vertical intercept.
  • Any number a for which f(a) = 0 is called the zero of the function.
  • You should be able to interpret the slope and intercepts of the function in the context given.

Problems to review:

Homework assignments from each section

Quizzes from chapter 1

More exercises: page 131-136 (chapter review) # 1-3, 5-9, 14-21, 30-33, 37-41, 44-50, 51-59 odd, 62-65.

Also Try:

x / y
-1 / 95
0 / 88
1 / 81
2 / 74
3 / 67

1. Using the following table, determine if y is a function of x. Is x a function of y?

Explain your reasoning.

2. Given the function,, find D(2), D(-1), D(x+1)

3. Write the equation of the line that passes through the points (3,4) and (1,-2).

4. An appliance repairman charges $50 for a service call and $15 for each hour spent on the job. Write a model for the money the repairman makes as a function of time spent on the job.

5. The area of lawn remaining, (in square yards), after x number of hours spent mowing is written as.

a) Name the slope and interpret its meaning in context.

b) Name the vertical intercept and interpret its meaning in context.