Answer:
Explanation:
To transform the function f(x)=|x| to fit a given set of data, we need to adjust the graph of f(x) by applying various transformations, such as shifts, reflections, and stretches. Here are some possible ways to transform f(x) to fit the data:
Vertical stretch: Multiply the entire function by a positive constant to stretch the graph vertically. For example, if the data points are all twice as large as the corresponding values of f(x), we can write the new function as g(x) = 2| x |.
Horizontal shift: Move the entire graph of f(x) left or right by adding or subtracting a constant from x. For example, if the data points are all shifted 2 units to the right of the corresponding values of f(x), we can write the new function as g(x) = | x - 2 |.
Vertical shift: Move the entire graph of f(x) up or down by adding or subtracting a constant from f(x). For example, if the data points are all 3 units above the corresponding values of f(x), we can write the new function as g(x) = | x | + 3.
Reflection: Reflect the entire graph of f(x) across the x-axis by changing the sign of the function. For example, if the data points are all below the x-axis, we can write the new function as g(x) = -| x |.
Combination: Combine any of the above transformations to adjust the graph of f(x) to fit the data more precisely. For example, if the data points are shifted 3 units to the left and 2 units above the corresponding values of f(x), we can write the new function as g(x) = | x + 3 | + 2.