HallsofIvy said:
A graph is a visual representation of a function that shows the relationship between the input and output values. The inverse of a function is another function that reverses the input and output values of the original function.
To evaluate f(2) and f(-2) on a graph, you need to locate the points with x-coordinates 2 and -2 on the x-axis. Then, you can find the corresponding y-coordinates on the y-axis. The points where the vertical lines through x=2 and x=-2 intersect the graph will give you the values of f(2) and f(-2).
f(2) and f(-2) represent the output values of a function when the input values are 2 and -2, respectively. In other words, they represent the y-coordinates of the points on the graph where the vertical lines through x=2 and x=-2 intersect the function.
A graph is symmetric about the line y=x if the inverse of the function is the same as the original function. This means that if you swap the x and y values of a point on the graph, it will still lie on the graph. You can also check for symmetry by folding the graph along the line y=x. If the two halves of the graph match up perfectly, then it is symmetric about the line y=x.
No, a graph and its inverse can only intersect once. This is because the inverse function reverses the input and output values of the original function, so any point that lies on both functions would have the same input and output values, making it the same point. Therefore, they can only intersect once at the point where x=y.