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

Expert Answers

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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 Value).  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.

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