## Introduction

In mathematics, reflection across the y-axis, denoted by the symbol ⟳ {\displaystyle \reflectbox {*{\rlap {}*{\mathrm {y} }}}}, is a linear transformation that produces a mirror image of a figure relative to the y-axis. That is, for any point (x, y) on the graph of a function, (x, –y) is also on the graph.

If the equation of a straight line is y = mx + b, then the equation of its reflection across the y-axis is –y = mx + b.

The function f(x) = x has a reflection across the y-axis of f(–x) = –x. The function f(x) = –x has a reflection across the y-axis of f(–x) = x.

## What is a function?

A function is a set of ordered pairs, where each element in the set corresponds to a unique output. In other words, for every input, there is only one output. A function can be represented using a graph on a coordinate plane. The inputs are graphed on the x-axis, and outputs are graphed on the y-axis. In order to determine if a graph is a function, we can use the Vertical Line Test.

## What is a graph of a function?

A graph of a function is a visual representation of how that function behaves. In other words, it shows the input/output pairs for that function. For example, the graph of the cosine function looks like this:

As you can see, for every x value, there is a corresponding y value. For instance, when x is 0, y is 1; when x is π/2, y is 0; and so on.

You can also use a graph to visualize how a function changes over time. For instance, the following graph shows what happens to the cosine function as x increases:

As you can see, as x gets bigger and bigger, the cosine function gets closer and closer to 0.

## What is the y-axis?

The y-axis is the vertical line through the origin in the coordinate plane. Its name comes from its definition in mathematics, where it is traditionally used as the axis of ordinates, or vertical axes, of a graph.

## What is the x-axis?

The x-axis is the horizontal line that runs from left to right on a graph. It is also the line that is used to measure how far along a graph something is. The x-axis is also known as the abscissa.

## What is the origin?

To understand what the origin is, we need to first understand what a graph is. A graph is a way of representing data, usually in the form of a line or curve. The origin is the point where the line or curve intersects the x-axis and y-axis. In other words, it is the point where the line or curve starts.

The origin is important because it is the starting point for all other points on the graph. For example, if we are graphing a line that goes from left to right, the origin will be the point where the line starts (on the left). From there, we can determine which way the line goes and how long it is.

There are two types of origins: absolute and relative. An absolute origin is defined as a specific point in space, such as (0,0). A relative origin is defined as a point that is relative to another point, such as (5,5). In most cases, we use an absolute origin because it is easier to work with.

The image below shows what an absolute and relative origin would look like on a graph:

As you can see, an absolute origin is easier to work with because all other points on the graph are based on that one specific point. With a relative origin, points can be based on any other point on the graph, which can make things more confusing.

## What is the range?

The range is the difference between the maximum and minimum values of a function. In other words, it is the length of the “span” of the function’s graph. To find the range of a cosine function, we need to find the minimum and maximum values of y. The function y = cos x has a range of [-1, 1]. This means that the graph of y = cos x will never be below the y-axis (values will never be less than -1) and will never be above the y-axis (values will never be greater than 1). The range can also be written as [1, -1], which is just another way of saying that the maximum value is 1 and the minimum value is -1.

## What is the domain?

The domain is the set of all values of x for which the graph of y cos x will be a valid reflection across the y-axis. In other words, it is the set of all values of x for which y cos x is defined.

## What is a function’s inverse?

The inverse of a function is a function that “undoes” the original function. In other words, the inverse of a function f(x) is a function g(x) such that the composition f(g(x)) = x, for all values of x where both sides of the equation are defined. For example, the inverse of the function f(x) = 2x + 1 is the function g(x) = (x – 1)/2, because 2((x – 1)/2) + 1 = x.

## What is reflected across the y-axis?

The y-axis is a line that represents the numbers on the vertical axis of a graph. It is sometimes called the “y-coordinate axis.” Anything that is reflected across the y-axis will have its sign changed. For example, if a point is reflected across the y-axis, its y-coordinate will change from positive to negative (or vice versa).

## Conclusion

In conclusion, reflecting the graph of y cos x across the y-axis is the same as not reflecting it at all.