How do you find the reflection of a function?
Reflections. A function can be reflected about an axis by multiplying by negative one. To reflect about the y-axis, multiply every x by -1 to get -x. To reflect about the x-axis, multiply f(x) by -1 to get -f(x).
How do you find the point of discontinuity of the greatest integer function?
Find all the points of discontinuity of the greatest integer function defined by `f(x) = [x]` where `[x]` denotes the greatest integer less than or equal to x. Find all the points of discontinuity of the greatest integer function defined by f(x)= [x], where [x] denotes the greatest integer less than or equal to x.
How do you reflect over the y-axis transformation?
The rule for a reflection over the y -axis is (x,y)→(−x,y) .
What happens when a function is reflected?
Suppose we have a function, f(x), with part of its graph below the x-axis. Then |f(x)| takes that part that is below the x-axis and reflects it over the x-axis to make it positive.
How are translations and reflections represented as a function?
How are translations and reflections represented as a function? A vertical reflection is given by the equation y=−f(x) and results in the curve being “reflected” across the x-axis. A horizontal reflection is given by the equation y=f (−x) and results in the curve being “reflected” across the y-axis.
Where is the greatest integer function not differentiable?
Greatest integer function isn’t continuous at the integers level and any function which is discontinuous at the integer value, will be non−differentiable at that point. As the value jumps at each integral value, therefore, it is discontinuous at each integral value.
Why is the greatest integer function not continuous?
Since L.H.L, R.H.L and the value of function at any integer n∈ are not equal therefore the greatest integer function is not continuous at integer points.
Is the greatest integer function continuous or discontinuous?
continuous
Note that the greatest integer function is continuous from the right and from the left at any noninteger value of x.
What is reflection over the y-axis?
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse.
How do you mirror a function about the y-axis?
We can reflect the graph of any function f about the x-axis by graphing y=-f(x) and we can reflect it about the y-axis by graphing y=f(-x). We can even reflect it about both axes by graphing y=-f(-x).