The function of the image sent is y = x. This is a parabola, specifically a symmetric parabola because its axis of symmetry is the y-axis.
Here are some key features of parabolas:
Parabolas have a single focus and a single directrix.
The distance between a point on the parabola and the focus is equal to the distance between that point and the directrix.
Parabolas open either upwards or downwards.
Parabolas are smooth curves that never intersect themselves.
The graph in the image is a parabola because it has all of these features. It opens upwards, has a single axis of symmetry, and is a smooth curve that never intersects itself.
The function of the image sent is y = x. It is a linear function, which means that its graph is a straight line. The slope of the line is 1, which means that for every 1 unit increase in x, there is a corresponding 1 unit increase in y.
The y-intercept of the line is 0, which means that the line passes through the origin (0, 0).
To graph the function y = x, we can plot two points on the coordinate plane and then draw a straight line through those points.
For example, we can plot the points (0, 0) and (1, 1). When we draw a line through these two points, we get the graph of y = x.
The graph of y = x has several interesting properties.
First, it is symmetrical about the line y = x. This means that if we reflect the graph across the line y = x, we get the same graph back.
Second, the graph of y = x is the bisector of the first and third quadrants. This means that any point on the graph of y = x is equidistant from the x-axis and the y-axis.
The graph of y = x is a very important function in mathematics. It is used in many different areas, such as geometry, algebra, and trigonometry. For example, the graph of y = x can be used to solve linear equations, find the slope and y-intercept of a line, and calculate the area of a triangle.