f(x) = |x| + 2
To find the equation for the function f(x) = |x| + 2, let’s break it down
To find the equation for the function f(x) = |x| + 2, let’s break it down.
The absolute value function, denoted as |x|, is defined as the distance between a number x and the origin (0) on the number line. The absolute value function always returns a non-negative value or zero.
In this case, f(x) = |x| + 2 means that we take the absolute value of x, and then add 2 to it.
Let’s consider a few scenarios to understand how this function behaves:
1. If x = 0, then |x| = |0| = 0. Thus, f(0) = 0 + 2 = 2.
2. If x > 0, then |x| = x. In this case, f(x) = |x| + 2 = x + 2. This means that for any positive value of x, the function increases linearly with a slope of 1, starting from a y-intercept of 2.
3. If x < 0, then |x| = -x. In this case, f(x) = |x| + 2 = -x + 2. Here, as x becomes more negative, the function also increases linearly with a slope of -1, starting from a y-intercept of 2. So, the graph of this function consists of two linear segments: one increasing with a slope of 1 for positive values of x, and the other increasing with a slope of -1 for negative values of x. The graph has a V shape with the vertex at (0,2) and extends indefinitely in both the positive and negative directions.
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