if f(x) is an even function, then f(x) is symmetric with respect to y-axis

if f(x) is odd function, then f(x) is symmetric with respect to x-axis

Now, if you have done PART C. Tell me which one is symmetric with respect to y-axis. Which one is symmetric with respect to x-axis.

So, Let's try some exercises to test your understanding about function:

__Question 1:__

__Question 2:__

__Question 3:__

__Question 4:__

__Question 5:__

Here are some parent functions that are introduced by the textbook:

I think you will have no problem dealing with exercises related to constant or linear. So we will try to deal with Absolute Value and Quaratic

**Keep in mind:**

```
Step 1: Find the linear group.
Step 2: Find the vertex.(Linear group = 0)
Step 3: Transformation
```

Let's try some example of identifying the linear group of these functions:

$g(x) = |x+2| - 1$

Ans: Linear group is x+2

$f(x) = 2 - \frac{5}{2}|x-7|$

Ans: Linear group is x-7

$f(x) = (x-5)^2 + 3$

Ans: Linear group is x-5

$h(x) = 3(2x+3)^2 -2$

Ans: Linear group is 2x+3

```
To find vertex:
a) Let (linear group) = 0
=> Find x-value (This is vertex's x-value)
b) Find y-value of vertex by plugging x-value into a function
```

$g(x) = |x+2| - 1$

x + 2 = 0 => x = -2

When x = -2 => g(-2) = -1

So vertex is (-2,-1)

$f(x) = 2 - \frac{5}{2}|x-7|$

x - 7 = 0 => x = 7

When x = 7 => f(7) = 2

So vertex is (7,2)

$f(x) = (x-5)^2 + 3$

Now, you can do it in your head:

So vertex is (5,3)

$h(x) = 3(2x+3)^2 -2$

So vertex is (-3/2, -2)

$g(x) = |x+2| - 1$

Since the vertex that we find is (-2,-1), we can see that the vertext has already tells us how the graph will move:

x = -2 means the original graph (orange color) will move to the left 2 unit y = -1 mneas the orginal graph (orange color) will move down 1 unit

Basically, the original graph move to the left 2 unit and move down 1 unit.

(Do you see the vertex of the original graph which is (0,0) has moved to (-2,-1) ?)

$f(x) = 2 - \frac{5}{2}|x-7|$

Now we can guess our vertex will move from (0,0) to (7,2)

BE CAREFUL! We have the scale (5/2) in front of linear group. So do it slowly:

You can compare the final transformation to the original graph.

The whole process could be explained as: The original graph flips upside down, scale with -5/2, then the graph moves along with the vertex from (0,0) to (7,2)

$f(x) = (x-5)^2 + 3$

Same things are applied as the above two examples:

Notice that: when we don't have the scale factor, the graph just move from the original vertex to the vertex that we find ( In this case, move from (0,0) to (5,3))

$h(x) = 3(2x+3)^2 -2$

BE CAREFUL! DO YOU NOTICE THE SCALE FACTOR OF 2 INSIDE THE LINEAR GROUP AND THE SCALE OF 3 OUTSIDE THE LINEAR GROUP.

The original graph is orange. The transformation graph is green.

You do not need to show work, just graph all the transformation and vertex ( I will teach you how to write your results formally later):

__Question 1:__

$f(x) = |1-x| -5$

__Question 2:__

$f(x) = |5-\frac{9x}{8}| +4$

__Question 3:__

$f(x) = 3 -(x +2)^2$

__Question 4:__

$f(x) = 2 + 3(5x + 1)^2$

__Question 5 and 6 are difficult. However, I have shown you how to deal with these types of problems. Try to do these two questions and I will go over these again next week.__

__Question 5:__

$f(x) = x^2 + 2x$

__Question 6:__

$f(x) = 3x^2 + x + 1$

In [ ]:

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