We're glad you stopped by On a coordinate plane an absolute value graph has a vertex at 1 3 Which equation represents the function graphed on the coordinate plane A. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
The equation that represents the function graphed on the coordinate plane with a vertex at (1, 3) is g(x) = |x - 1| + 3.
To explain this concept, let's break it down:
- The vertex of an absolute value graph is the point where the graph changes direction. In this case, the vertex is at (1, 3).
- The equation for an absolute value function is of the form g(x) = |x - h| + k, where (h, k) represents the vertex.
- In the given equation, h = 1 and k = 3. This means that the graph will be shifted horizontally by 1 unit to the right and vertically by 3 units up from the usual y = |x| graph.
- The absolute value function g(x) = |x - 1| + 3 represents the graph that has a vertex at (1, 3). It means that the function takes the absolute value of the difference between x and 1, and then adds 3 to it.
- For example, when x = 0, the absolute value of (0 - 1) is 1, and when we add 3 to it, we get a y-value of 4. So, one point on the graph is (0, 4).
- Similarly, when x = 2, the absolute value of (2 - 1) is 1, and when we add 3 to it, we get a y-value of 4. So, another point on the graph is (2, 4).
- By substituting different x-values into the equation, we can find more points and sketch the graph of the function.
In summary, the equation g(x) = |x - 1| + 3 represents the absolute value function with a vertex at (1, 3) on the coordinate plane.
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