The graph shows f(x). The absolute value function g(x) is described in the table. The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3. xg(x) −15 04 13 22 33 If g(x) = f(x k), what is the value of k? k = −2 k is equal to negative one half k is equal to one half k = 2

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30-07-2024
Mathematics

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The graph shows f(x). The absolute value function g(x) is described in the table. The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3. xg(x) −15 04 13 22 33 If g(x) = f(x k), what is the value of k? k = −2 k is equal to negative one half k is equal to one half k = 2

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Answer:

Let's analyze the problem:

Understanding the given information:

We hadve a graph of an absolute value function f(x) with a vertex at (0, 2).

We have a table of values for another absolute value function g(x).

The relationship between f(x) and g(x) is given by g(x) = f(x + k).

Goal:

Find the value of k.

Analysis:

The key to solving this problem lies in understanding the transformation represented by g(x) = f(x + k). This transformation is a horizontal shift of the graph of f(x).

If k is positive, the graph of f(x) is shifted k units to the left.

If k is negative, the graph of f(x) is shifted k units to the right.

Since we don't have the exact values of g(x) for specific x values, we can't pinpoint the exact shift. However, we can make an educated guess based on the general shape of absolute value functions.

Possible solution:

Given that the vertex of f(x) is at (0, 2) and the table for g(x) starts with x = -1, it's likely that g(x) is a shifted version of f(x) to the right. This would indicate a negative value for k.

Based on this analysis, the most likely answer is k = -2.

However, without the exact values of g(x) for different x values, we cannot be completely certain.

To get a definitive answer, i would need more information about the function g(x), such as specific points on the graph or additional values in the table.