Questions: Which could be the graph of f(x) = x - h + k if h and k are both positive?

Transcript text: Which could be the graph of f(x) = |x - h| + k if h and k are both positive?

Solution

Solution Steps

Step 1: Analyze the function

The function \(f(x) = |x - h| + k\) represents a V-shaped graph. The vertex of this graph is at the point \((h, k)\).

Step 2: Consider the conditions

Since both \(h\) and \(k\) are positive, the vertex of the V-shaped graph must be in the first quadrant (where both x and y coordinates are positive).

Step 3: Identify the correct graph

The first graph has a vertex in the first quadrant. The second graph has a vertex in the fourth quadrant. The third graph has a vertex in the first quadrant. The fourth graph shows a linear graph, not a V-shape.

Final Answer

The first and third graphs could represent the function \(f(x) = |x - h| + k\) if \(h\) and \(k\) are both positive.

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