Write the equation of the function that has a graph the shape of y=/x/ ,reflected about the x-axis and shifted down 1 unit.
Do you mean y = |x| the absolute value of x?
For the shifting down by one unit, subtract 1. For the reflection about the x axis, change the sign.
Thus y = -|x| -1
y is never greater than -1, and decreases with slope +/-1 on either side of x=0
Thank You
To find the equation of the function with the graph of y = |x|, reflected about the x-axis and shifted down 1 unit, we can start with the original equation y = |x| and apply the transformations one by one.
1. Reflection about the x-axis:
To reflect a graph about the x-axis, we change the sign of the y-values. Therefore, the reflection of y = |x| about the x-axis is y = -|x|.
2. Shifting down 1 unit:
To shift the graph down 1 unit, we subtract 1 from the y-values. Therefore, the final equation is y = -|x| - 1.
So, the equation of the function with the desired graph is y = -|x| - 1.