Question

Which could be the graph of f(x) = |x - h| + k if h and k are both positive? On a coordinate plane, an absolute value graph has a vertex at (2, 1). On a coordinate plane, an absolute value graph has a vertex at (1, negative 4). On a coordinate plane, an absolute value graph has a vertex at (negative 3, 2). On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 5).

Answer 1

The graph of f(x) = |x - h| + k with h and k both positive would have its vertex in the first quadrant where both x and y values are positive. Of the given options, the graph with a vertex at (2, 1) is the correct one, as it's the only vertex with both coordinates being positive.

Step-by-step explanation:

The question is asking which graph could represent the function f(x) = |x - h| + k given that h and k are both positive numbers. The graph of an absolute value function is typically a V-shaped curve, with the vertex representing the point (h, k). Since h and k are positive, the vertex of the graph should be in the first quadrant of the coordinate plane, where both x and y values are positive.

Now, let's evaluate the provided vertex options:

• A vertex at (2, 1) would be correct since both coordinates are positive.
• A vertex at (1, -4), (-3, 2), and (-4, -5) would not be correct because either one or both coordinates are negative, which is not possible if h and k are positive.

Therefore, the graph of f(x) = |x - h| + k with h and k being positive could have a vertex at (2, 1).