# How do you graph # f(x) = |x| + |x + 2| #?

##### 1 Answer

#### Answer:

Please read the explanation.

#### Explanation:

**Given:**

We need to **graph** this **absolute value function**.

We will assign the values for

To find the corresponding

Please look at the table of values that contains all values for **Ordered Pair** to facilitate graphing.

The corresponding graph is given below:

**Observations:**

For the **parent function**

**Vertex** is at

**Vertex** is the **minimum point** on the graph.

**Axis of Symmetry** is at

A **translation** is a transformation that shifts a graph **horizontally** or **vertically**, but does not change the **orientation of the graph.**

Please refer to the graph to observe the following:

**Domain** of the function

is

**Range** of the function

is

**Extreme Points** are **none** for

**Critical Points**:

**Critical points** are points **where the function is defined** and **its derivative is zero or undefined.**

**Critical Points** are at

**X and Y Intercepts:**

**x-axis interception points of **

**y-axis interception points of **

The graph of

has **shifted up (a.k.a. Vertical Translation)** by two units comparing to the graph of the **parent function**