UNIT 1 TEST REVIEW ALGEBRA II

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

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

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

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

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

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 )

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

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.

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 )

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)

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).

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

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

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

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

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