Questions: Identify the vertex and graph each function. State the domain a 1. f(x)=2x-6 Vertex: D: R :

Transcript text: Identify the vertex and graph each function. State the domain a 1. $f(x)=2|x-6|$ Vertex: D: $R$ :

Solution

Solution Steps

Step 1: Find the vertex

The given function is _f(x) = 2|x - 6|_. The general form of an absolute value function is _f(x) = a|x - h| + k_, where (h, k) is the vertex. In this case, h = 6 and k = 0. Thus, the vertex is (6, 0).

Step 2: Graph the function

Plot the vertex (6,0). The "a" value is 2, signifying a vertical stretch by a factor of 2. This means that from the vertex, the graph goes up two units for every one unit to the left or right.

Step 3: State the domain and range

The domain is all real numbers, because we can plug in any value of _x_. The range is _y_ ≥ 0 because the lowest point on the graph is at _y_ = 0 and the graph opens upwards.

Final Answer:

Vertex: (6, 0) Domain: R (all real numbers) Range: R: (0, ∞)

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