Question

In Exercises 39–50, 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| +1

Accepted Answer

Identify the given functions: $$ f(x) = |x| $$ and $$ g(x) = |x| + 1 . $$Create a table of values for $$ x $$ from -2 to 2 for both functions. For each $$ x $$, calculate $$ f(x) = |x| $$ and $$ g(x) = |x| + 1 . $$Plot the points for $$ f(x)  on $$the coordinate plane using the values from the table. Connect these points to form the graph of $$ f(x) = |x| $$, which is a V-shaped graph with its vertex at the origin (0,0). Plot the points for $$ g(x)  on $$the same coordinate plane using the values from the table. Connect these points to form the graph of $$ g(x) = |x| + 1 $$, which will also be a V-shaped graph but shifted vertically. Compare the two graphs and describe the transformation: since $$ g(x) = f(x) + 1 $$, the graph of $$ g  is $$the graph of $$ f $$ shifted upward by 1 unit.

In Exercises 39–50, 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| +1

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Key Concepts

Absolute Value Function

Function Transformation - Vertical Shift

Graphing with Integer Inputs