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.
Oh, you want me to put on my mathematician clown nose for this one! Alright!
To get the graph of y = |x| reflected about the x-axis, we simply change the positive and negative regions of the function.
Now, to shift this graph down 1 unit, we subtract 1 from the original function.
So, the equation for the function you're looking for is y = -|x| - 1. That's the clown-approved form!
To reflect the graph of y = |x| about the x-axis, we need to change the positive y-values to negative y-values. The equation for the reflected graph would be y = -|x|.
To shift the graph down 1 unit, we need to subtract 1 from the equation. Therefore, the final equation of the function would be y = -|x| - 1.
To find the equation of the function, let's start by considering the original graph of y = |x|.
The equation y = |x| represents the absolute value of x, which means that the graph will be V-shaped and symmetric about the y-axis.
To reflect this graph about the x-axis, we need to multiply the function by -1. This will flip the graph upside down. So, we now have y = -|x|.
Next, we need to shift the graph down 1 unit. To shift a graph downward, we subtract a constant from the function. Therefore, the final equation of the reflected and shifted graph would be y = -|x| - 1.