Question

Graph y = │x + 2│.

Answer 1

To graph the function y = │x + 2│, we can start by considering different cases for the value of x.

If x ≥ -2:
In this case, the absolute value │x + 2│ simplifies to x + 2, so the equation becomes y = x + 2.

If x < -2:
In this case, the absolute value │x + 2│ makes x + 2 negative, so the equation becomes y = -(x + 2).

By considering both cases, we can construct the graph:

For x ≥ -2:
When x is greater than or equal to -2, the equation y = x + 2 represents a linear function with a positive slope.

For x < -2:
When x is less than -2, the equation y = -(x + 2) represents a linear function with a negative slope.

In both cases, the vertical intercept is at (0, 2).

Combining both cases, the graph of y = │x + 2│ will have a V-shape, with the vertex at (-2, 0).

Here is a visual representation of the graph:

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