What does it mean when a graph is symmetric to the y-axis?

Functions can be symmetrical about the y-axis, which means that if we reflect their graph about the y-axis we will get the same graph. There are other functions that we can reflect about both the x- and y-axis and get the same graph. These are two types of symmetry we call even and odd functions.

What YX means?

Chapter 3. Note: A function defines one variable in terms of another. The statement “y is a function of x” (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. “x causes y”), but does not *necessarily* exist.

How do you tell if a function is symmetric with respect to the origin?

Another way to visualize origin symmetry is to imagine a reflection about the x-axis, followed by a reflection across the y-axis. If this leaves the graph of the function unchanged, the graph is symmetric with respect to the origin.

How do you determine if a graph is symmetric with respect to the y-axis?

To check for symmetry with respect to the y-axis, just replace x with -x 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 y-axis.

Is the absolute value function even?

It is an even function.

What happens when you reflect over Y X?

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).

What functions are symmetric with respect to y-axis?

A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function.

Are odd functions symmetric about the y-axis?

An even function has reflection symmetry about the y-axis. An odd function has rotational symmetry about the origin.

What does -y=-f(x) mean?

y=-f(x) therefore denotes the negative of the function, the negative of the entire f(x). As such, it would look more like -(f(x)) if you wanted it to be more clear, the exact same as writing -y=f(x).

What does y equals 2 to the X look like?

We call the y equals 2 to the x is one of our parent functions and has this shape sort of an upward sweeping curve passes through the point 0 1, and it’s got a horizontal asymptote on the x axis y=0. Let’s plot a few points. We’ve got u and 2 to the u.

What is the reflection y = f (-x)?

The Reflection y = f (-x) – Concept. There are different types of transformations and their graphs, one of which is a math reflection across the y-axis. If we get the same function from a math reflection, it is a symmetrical function, specifically even. A math reflection flips a graph over the y-axis, and is of the form y = f (-x).