How do you know if a graph is symmetric to the x-axis?

How do you know if a graph is symmetric to the x-axis?

To check for symmetry with respect to the x-axis, just replace y with -y and see if you still get the same equation. If you do get the same equation, then the graph is symmetric with respect to the x-axis.

Does an exponential graph have symmetry?

The power function graphs as a parabola, which is symmetrical about the y axis, while the exponential function has no symmetry. The power function has no asymptote (a line that a curve approaches ever …

How do you know if a graph is symmetric or not?

A graph is symmetric with respect to a line if reflecting the graph over that line leaves the graph unchanged. This line is called an axis of symmetry of the graph. A graph is symmetric with respect to the x-axis if whenever a point is on the graph the point is also on the graph.

Does E X have symmetry?

Since ex=ex e x = e x , the function is even. Since the function is even, it is symmetric about the y-axis.

How do you know if a function is symmetric?

Algebraically check for symmetry with respect to the x-axis, y axis, and the origin. For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

Can a function have symmetry over the x-axis?

Note: By definition, no function can be symmetric about the x-axis (or any other horizontal line), since anything that is mirrored around a horizontal line will violate the Vertical Line Test.

How do you show a function is symmetric?

A function can be symmetric about a line. when a function is symmetric about x-axis then, f(y)=f(−y) f ( y ) = f ( − y ) . when a function is symmetric about y-axis then, f(x)=f(−x) f ( x ) = f ( − x ) . when a function is symmetric about origin then, f(x,y)=f(−x,−y) f ( x , y ) = f ( − x , − y ) .

Is Lnx the same as ex?

Properties • ln x is the inverse of ex: ∀x > 0, E ◦ L = eln x = x. graph(ex) is the reflection of graph(ln x) by line y = x.

How to test the symmetry of a graph?

Test for symmetry: Even and odd functions. Symmetry, then, depends on the behavior of f(x) on the other side of the y-axis — at minus-x : f(−x). Here is the test: If f(−x) = f(x), then the graph of f(x) is symmetrical with respect to . To see the answer, pass your mouse over the colored area.

Is the graph f ( x ) symmetrical with respect to the Y axis?

Answer. f(x) is even—it is symmetrical with respect to the y-axis—because f(−x) = f(x). Note: A polynomial will be an even function when all the exponents are even. A polynomial will be an odd function when all the exponents are odd. But there are even and odd functions that are not polynomials.

Which is symmetric with respect to the x axis?

If a function is symmetric with respect to the x -axis, then f (x) = – f (x) . The following graph is symmetric with respect to the y -axis ( x = 0 ). Note that if (x, y) is a point on the graph, then (- x, y) is also a point on the graph.

When is a graph said to be symmetric about the origin?

A graph is said to be symmetric about the origin if whenever (a,b) ( a, b) is on the graph then so is (−a,−b) ( − a, − b). Here is a sketch of a graph that is symmetric about the origin.