1. EOC Preparation Unit Objective 2
Algebra 1
Independent and Dependent Quantities
Independent and Dependent Quantities must be variables (letters), not constants (numbers).
Independent Quantities are often quantities that cannot be controlled
Dependent Quantities change as a result of the Independent Quantities
Algebra 1
Algebra 1
Student Copy
EOC Preparation Unit
Objective 2
EOC Preparation Unit
Objective 2
EOC Preparation Unit
Objective 2:
1, Ab1A

2. Parent Functions y = x² y = x
There are two parent functions on the EOC test:
Linear
Quadratic
y = x²
y = x
Opens up
Vertex at (0, 0)
y axis is axis of symmetry
2, Ab2A

3. Domain and Range Domain is the set of all x values
Range is the set of all y values
To find domain: examine the right and left boundaries of the function
To find range: examine the top and bottom boundaries of the function
Whenever a function has two boundaries, both signs should be less than (< or ≤).
2, Ab2B

4. Domain and Range, cont… Example of finding the Domain Domain: -3 2
2, Ab2B

5. Domain and Range, cont… Example of finding the Range Range 5 -4
____ ≤ y < ____ 5 -4
2, Ab2B

6. Interpreting Graphs Pay attention to labels on x and y axes
A straight line indicates constant rate of change (slope)
A curved line indicates a changing rate
More than one straight lines indicates rapidly changing constant rates
2, Ab2C

7. Interpreting Graphs, cont…
The slope of lines indicates speed
Steep line means rapid speed
Flat line means no movement
No movement
1000 ft in 1 min fastest speed
1000 ft in 2 min or 500 ft per min
500 ft in 2 min or 250 ft per min
500 ft in 1 min
2, Ab2C

8. Scatter Plots
Correlation
Positive Negative No
2, Ab2D

9. Using symbols Focus on the meaning of words in a mathematical context
For Example:
More, more than, in addition, …. Mean … +
Less, less than, difference …. Mean … -
Times, per, each, … Mean … x
Per, each, dividend … Mean … ÷
Is or other verbs … Mean … =
The goal is to turn a sentence into an equation.
3, Ac3A

10. Using symbols, cont… Here is a simple example:
The area of a circle is equivalent to pi times the radius squared. A = π • r
So, you would look for the answer A = πr²
3, Ac3A

11. Patterns
Given a geometric sequence, you must determine the equation for the function.
Make a table to represent the sequence
Use STAT to calculate the answer
Find the answer that fits the calculator answer
3, Ac3B

12. Patterns, cont… Here’s an example: Make a table 1 2 4 3 9 16 Figure
# of squares 1 2 4 3 9 16
3, Ac3B

13. Patterns, cont… Now use STAT to calculate the equation.
STAT ENTER NUMBERS STAT 
(x in L1 & y in L2)
5, ENTER
Look for an answer that has an equation like y = x².
3, Ac3B

14. Solving Equations and Inequalities
Substitute given values
Use inverse operations to solve
Example: If (2.25, y) is a solution to the equation 4x – 2y = 8, what is the value of y?
4x – 2y = 8
4(2.25) – 2y = 8
y = ½
9 – 2y = 8 -9 -9
– 2y = -1 -2 -2
3, Ab4A

15. Solving Equations and Inequalities, cont…
Convert inequalities from Standard form (Ax + By > C) to y = mx + b form.
Use the same steps as you would for an equation, but remember that if you multiply or divide by a negative number, you must flip the inequality sign!
Example: 4x – 2y ≤ 5
- 4x
- 4x
-2y ≤ -4x + 5
Because you divided by a negative, you must flip the ≤ to ! -2 -2 -2
y  2x – 2.5
3, Ab4A

16. Solving Equations and Inequalities, cont…
Given a function like y = 3x² + 2x – 4 and a set of independent variables like {-1, 0, 1, 2} and asked to find a corresponding dependent variable
Remember that independent variables represent the x values and dependent variables represent y values
Just use the calculator to graph the function and look at the table to identify the corresponding y values
3, Ab4A

17. Solving Equations and Inequalities, cont…
Example: A function is described by the equation y = 3x² + 2x – 4, in which y is dependent on x. If a value for the independent variable is selected from the set {-1, 0, 1, 2}, which of the following is a corresponding dependent value?
The answer must be from the y values that correspond to the x values listed in the question. So, the answer must be one of {-3, -4, 1, 12}.
3, Ab4A

18. Simplifying Expressions
Use properties to simplify completely
Example: Which expression is equivalent to (5t – 4)6t – (5t – 4)(t + 1)?
Multiply to eliminate parentheses
30t²
- 24t
- (
5t²
+5t
- 4t
- 4)
30t² - 24t – 5t² - 5t + 4t + 4
Combine like terms
25t²
-25t
+ 4
3, Ab4B