1. UNIT 1 TEST REVIEW ALGEBRA II

2. Investigating Functions
Make a table
Draw a graph
Find Domain and Range
Find the x and y intercepts

3. Making a Table Lets say you have the equation
Put the equation in your calculator under the Y = button and hit graph.
Now you know what your graph looks like.
If you hit 2nd GRAPH, the calculator will tell you the values for x and y.
You can also substitute the x values in your equation x -3 -2 -1 1 2 3 y 4 -4 -5

4. Making a Graph
Use your points from your table to draw the graph.

5. Finding Domain Look at your graph. Where does it start and end?
Look on the x-axis. Start on the left side, where does it start? Where does it end?
From the left, notice the arrow, it goes on forever. That means the domain starts at - ∞.
Look at the graph from the right, where does it stop? It doesn’t end. That means it ends at ∞.
You can write this domain two ways:
All x
[- ∞< x < ∞]
x axis

6. Finding Range Look at your graph. Where does it start and end?
Look on the y-axis. Start on the bottom, where does it start? Where does it end?
From the bottom, find the starting point. You can use the calculator under 2nd CALC (minimum).
Look at the graph from the top, where does it stop? It doesn’t end. That means it ends at ∞.
You can write this range two ways:
y≥-5
[-5≤ y < ∞]
y axis

7. Finding x intercept
To find the x intercept, you need to find where the graph crosses the x axis.
You can do this algebraically by setting y=0 and solving for x.
You can also do this in your calculator under 2nd CALC (zero).
This graph has 2
x intercepts (circled )

8. Finding x intercept algebraically
Set y = 0 and solve for x.
0 = x² = x² √5 =√ x² x= ±2.236
x intercepts (2.236, 0) and (-2.236, 0)

9. Finding x intercept on calculators
Graph your equation.
Go to 2nd CALC
Select #2: ZERO
It will ask “Left Bound.” Go to the left of where the graph crosses the x axis and hit enter.
It will ask “Right Bound.” Go to the right of where the graph crosses the x axis and hit enter.
It will ask “Guess.” Go to where you think the graph crosses the x axis and hit enter.
It will tell you’re your point. Write it as a coordinate (x,y).
Do the same for anywhere else the graph crosses the x axis.

10. Finding the y intercept
To find the y intercept, you need to find where the graph crosses the y axis.
You can do this algebraically by setting x=0 and solving for y.
You can also do this in your calculator under 2nd CALC (value).
y intercept (circled )

11. Finding y intercept algebraically
Set x = 0 and solve for y
y = (0)² - 5
y = 0 – 5
y = -5
y intercept is (0,-5)

12. Finding y intercept on calculators
Graph your equation.
Go to 2nd CALC
Select #2: VALUE
Type is 0 for x.
It will tell you’re your point. Write it as a coordinate (x,y).

13. Rules for Solving Equations
Simplify.
Fraction Bust
Combine Like Terms
Cross Multiply
Factor
Distribute
Isolate the variable (x).
Adding or subtracting
Multiplying or dividing
Squaring or finding the square root

14. Example 1 2x (3) -3 = 2 (x + 2) 6x – 3 = 2x + 4 +3 + 3 6x = 2x + 7
6x = 2x + 7
- 2x - 2x
4x = 7 x =

15. Example 2
Find the Least Common Denominator : 6
Multiply every term by 6 6 6 6
Multiply through and then simplify.
8 + 3x = 12x
8 = 9x

16. Example 3 2 (x – 2) = 3 (x – 4) 2x – 4 = 3x – 12 2x = 3x – 8 -x = -8
CROSS MULTIPLY
2 (x – 2) = 3 (x – 4)
2x – 4 = 3x – 12
2x = 3x – 8
-x = -8
x = 8
DISTRIBUTE
Add 4 to both sides
Subtract 3x from both sides
Get rid of the negative

17. Example 4 x² + 7x + 10 = 0 Use the diamond method
5 x 2 = 10 and = 7
(x+5)(x+2)= 0 Use Zero Product Property
x + 5 = 0 and x +2 = 0
x = -5, -2