Question

Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = |x|, g(x) = |x| − 2

Accepted Answer

Identify the given functions: $$f(x) = |x|$$ and $$g(x) = |x| - 2. $$Notice that $$g(x) is $$derived from $$f(x) by $$subtracting 2 from the output values. Create a table of values for $$x$$ starting from $$-2 to$$ $$2. $$For each $$x$$, calculate $$f(x) = |x|$$ and $$g(x) = |x| - 2. $$For example, when $$x = -2$$, $$f(-2) = |-2| = 2$$ and $$g(-2) = 2 - 2 = 0. $$Plot the points for both functions on the same coordinate system. For $$f(x)$$, plot points like $$(-2, 2)$$, $$(-1, 1)$$, $$(0, 0)$$, $$(1, 1)$$, and $$(2, 2). $$For $$g(x)$$, plot the corresponding points shifted down by 2 units, such as $$(-2, 0)$$, $$(-1, -1)$$, $$(0, -2)$$, $$(1, -1)$$, and $$(2, 0). $$Draw the graph of $$f(x) = |x|$$, which is a 'V' shape with its vertex at the origin $$(0,0). $$Then draw the graph of $$g(x) = |x| - 2$$, which has the same 'V' shape but shifted vertically downward by 2 units. Describe the relationship: The graph of $$g(x) is $$the graph of $$f(x)$$ shifted downward by 2 units. This vertical shift is due to the subtraction of 2 in the function $$g(x) = |x| - 2.$$

Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = |x|, g(x) = |x| − 2

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Key Concepts

Absolute Value Function

Function Transformation - Vertical Shift

Graphing Functions Using Integer Inputs