Which equation shows an absolute value function reflected over the x-axis, shifted left 3, up 2.
To find the equation of an absolute value function that is reflected over the x-axis, shifted left 3 units, and shifted up 2 units, we will start with the standard equation of an absolute value function and make the necessary adjustments.
The standard equation of an absolute value function is y = |x|.
To reflect the function over the x-axis, we need to multiply the entire equation by -1:
y = -|x|.
To shift the function left 3 units, we need to replace x with (x + 3):
y = -|x + 3|.
Finally, to shift the function up 2 units, we need to add 2 to the equation:
y = -|x + 3| + 2.
Therefore, the equation showing an absolute value function reflected over the x-axis, shifted left 3 units, and up 2 units is y = -|x + 3| + 2.