what is the equation for the axis of symmetry for the function f(x)=IxI?(absolute value)
the axis of symettry is x=0
what about if it was moved, say (x,y)-> (x+3, y-1)? i understand where the line is visually but i don't know how to write the equation
To find the equation for the axis of symmetry of the function f(x) = |x| (absolute value), we need to first understand what an axis of symmetry is.
An axis of symmetry is a vertical line that divides a graph into two mirror images. For functions with absolute value, the axis of symmetry is always the y-axis, which is the line x = 0.
Therefore, the equation for the axis of symmetry for the function f(x) = |x| is x = 0.
To find the equation for the axis of symmetry for the absolute value function f(x) = |x|, you need to understand the properties of absolute value functions.
The absolute value function |x| gives the distance of x from 0 on the number line. It always returns a positive value or zero, regardless of the input sign of x.
To determine the equation of the axis of symmetry, we need to find the line that divides the absolute value function into two symmetrical halves.
In the case of the absolute value function f(x) = |x|, the axis of symmetry is the y-axis or the line x = 0.
Therefore, the equation for the axis of symmetry is x = 0.
This means that any point on the y-axis will have its corresponding symmetric point on the opposite side of the line x = 0.