The equation that represents the graph is g(x) = |x + 4| - 10.
The correct option is B.
What is transformation on the graphs?
Let the functions f(x) and g(x) be two real functions.
And g (x) = f (x) + k, where k is real numbers.
The function can be sketched by shifting f (x), k units vertically.
The direction of shift can be found by the value of k:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
The function provided by the basic function f(x) and the constant
g(x) = f(x - k),
may be drawn by horizontally moving the f(x) k unit coordinates.
The shift's direction depends on the value of k. Specifically,
The base graph moves k units to the right if k > 0, and
The base graph moves k units to the left if k < 0.
Since the graph of the parent function is g(x) = |x|, the transformed graph is obtained by shifting it 4 units to the left and 10 units down. This can be achieved by applying the following transformations to the parent function:
Shift 4 units to the left: g(x + 4) = |x + 4|
Shift 10 units down: g(x + 4) - 10 = |x + 4| - 10
Therefore, the equation for the transformed function is g(x + 4) - 10 = |x + 4| - 10.
To learn more about the transformation on the graphs;
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