Notice that g(x) describes the absolute value of f(x).
A
a
Diagram:
Explanation: See solution.
B
b
Diagram:
Explanation: See solution.
Practice makes perfect
a
The parent function of f(x) is f(x)=|x|, which can be described as the graph of f(x)=x, but where the negative side of the y-axis has been reflected in the x-axis.
When we add or subtract a constant from a function's input, the resulting transformation is a horizontal translation. Subtracting 6 from the input results in a horizontal translation by 6 units to the right.
Adding or subtracting a constant to the output of the function shifts its graph up or down. In this case we are subtracting 4 from the output, which results in a vertical translation of 4 units in the negative direction.
Let's clean up the diagram.
b
From Part A, we have graphed f(x).
Examining the function of g(x), we notice that g(x) is the absolute value of f(x).
f(x)= |x-6|-4
g(x)=| |x-6|-4|
↓
g(x)=| fx|
When we calculate the absolute value of something, negative values changes signs and become positive. Examining the graph from Part A, we see that the function exhibits negative values in the following interval.
2
