1. Algebra Review

2. Due on Tuesday September 5th Evens or Odds only
Algebra Review
Review Packet
Due on Tuesday September 5th
Evens or Odds only

3. Algebra Review Combining Like Terms
Adding or subtracting terms within an expression or equation
Must have the same variable and exponent
Add or subtract the coefficient in the front only, exponent stays the same
Examples:

4. Algebra Review Multiplying Terms Multiply coefficients
If the same variable, add the exponents
Examples:
Dividing Terms
Divide coefficients
If the same variable, subtract the exponents

5. Algebra Review Solving Equations
Goal: To get the ____________ alone on one side of the equal sign.
Get common ___________ together
Always move constants farthest away from the variable first.
Always do the ______________ operation to cancel out and move to other side.
What you do to one side, you have to do to the other because, “Life’s not _______, but _____________ is!”
Examples:

6. Algebra Review
Practice

7. Algebra Review Distributive Property
The _______________ outside the parentheses must be distributed to each _______________ inside the parentheses.
A(B +C) = A(B) + A(C)
Examples:

8. Algebra Review Simplifying Equations
Combine terms with the ________________ variable.
Examples:

9. Algebra Review
Visualize Vocabulary!

10. Algebra Review
coordinate plane - A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis Ordered pair - A pair of numbers (x, y) that can be used to locate a point on a coordinate plane. The first number x indicates the distance to the left or right of the origin, and the second number y indicates the distance above or below the origin origin - The intersection of the x- and y-axes in a coordinate plane. The coordinates of the origin are (0, 0) x-axis - The horizontal axis in a coordinate plane y-axis - The vertical axis in a coordinate plane

11. Algebra Review
A relation is a set of ordered pairs (x, y) where x is the input value and y is the output value.
The domain is all possible inputs of a relation, and the range is all possible outputs of a relation.
For example, the given relation represents the number of whole-wheat cracker boxes sold and the money earned.
{(1, 4) , (2, 8) , (3, 12) , (4, 16) }.
Domain: {1, 2, 3, 4} Range: {2, 8, 12, 16}

12. Algebra Review
X-values, input values, independent variable, and domain are all the same
Y-values, output values, dependent variable, and range are all the same
Dependent variable depends on the independent variable

13. Algebra Review
A function is a type of relation in which there is only one output value for each input value. There is no repeat in x values / domain.
Function notation – a way of writing an equation that usually replaces y with f(x)
Reasonable domain and range = what makes sense

14. Algebra Review
A test, called the vertical line test, can be used to determine if a relation is a function.
“A relation is a function if and only if a vertical line does not pass through more than one point on the graph.”

15. Algebra Review 4 ways to express a function: Mapping diagram
Ordered pairs
Table
Graph

16. Algebra Review
For the following relation, the input, x, is the ages of boys and the output, y, is their corresponding height, in inches.
{(7, 41) , (8, 45) , (9, 49) , (10, 52) , (10, 53) , (11, 55) , (12, 59)}
Fill the values in the table.
Plot the points on the graph.
Complete the mapping diagram.
State the domain of the relation.
State the range of the relation.

17. Algebra Review

18. Algebra Review Graph the function for the given domain.
x + 3y = 15 D: {0, 3, 6, 9}
y = 2x D:{-2, 0, 2, 4}
-3x - 5y = 20 D:{-10, -5, 0, 5}

19. Algebra Review
Graph the function:
y = - 𝑥
x + y = 0
y = -4x + 2

20. Algebra Review
Linear Function: when graphed, forms a non-vertical straight line
Why must it be non-vertical?
Parent Function: the most basic function of a family of functions y = x

21. Algebra Review How can you write a linear function? 3 forms:
Standard form: Ax + By = C
A, B, and C are real numbers and A and B are not both 0.
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
Point-slope form: y – y1 = m(x – x1)
x1 and y1 are the coordinates of a point on the line

22. Algebra Review Intercepts
Y-intercept (b) – where the graph crosses the y-axis. X=0
X-intercept – where the graph crosses the x-axis. Y=0
Can be found by plugging 0 in for x or y, or using slope intercept form, or looking at a graph

23. Algebra Review Slope (m)
Same as the rate of change over a part of the domain
Slope = Rate of change = change in y = rise
change in x run
Slope formula: m = y2 – y1
x2 – x1
Slopes can be positive (leans right), negative (leans left), or zero (horizontal line).
Can also be identified in slope-intercept form.
Mr. Slope Face

24. Algebra Review

25. Algebra Review
Practice