# `f(x) = |x + 2|` Graph each function. Identify the domain and range.

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### 2 Answers

This problem is asking you to graph a function - more specifically, an absolute value function. Given that the function is written in terms of x - that indicates that the shape is going to be a v-shape (think absolute **V**alue). You can find points to help determine where the graph is located on the coordinate plane - most of the time it's easiest to plug in numbers like 0 or 1, or numbers that would create a zero inside the absolute value symbols - in this case - plug in a -2, - that will help you find the vertex (the point where the graph changes directions - from increasing to decreasing or vice versa). Then find a couple of points on both sides of -2, like -3, -4, -1, and 0. This will give you a set of points so that you can sketch the graph. This function includes other points (fractions, decimals) between those integers - a continuous function. The domain is asking for all of the possible x values (so look at the x-axis) which goes from left to right - and since the graph goes from left to right and continues in both directions - it is never ending or we use the word infinity - or All Real Numbers. The range is asking for the y values (so look at the y-axis) which goes up and down - and since the graph doesn't go below the x-axis - where y=0 and all the points of the graph are above the x-axis, the range would be all y values that are greater than of equal to 0.

`f(x) = |x+2|` , the the domain and range is given as follows

(i)Domain definition:

The domain of a function is the set of the input or argument values for which the function is real and defined.

In this function, The function has no undefined points, so the domain is

`-oo <x<oo` .

(ii)Range definition

It is the set of values of the dependent variable for which a function is defined.

For this function the interval has a minimum point at x= -2 with value f(x) = 0

so the range of `|x+2| is f(x) >= 0`

It can also be observed from the graph below: