f(x)=3^x and g(x)=(1/3)^x I put that they mirror each other, that they are symmetrical. I am obviously missing something important between the two
A symmetric graph is a graph in which the left and right sides are mirror images of each other. This means that if a point (x,y) is on the graph, then the point (-x,y) is also on the graph.
These two functions are symmetric because the exponent in each function can be changed to its opposite sign without changing the overall shape of the graph. This means that f(x) and g(x) will have the same y-values for opposite x-values, making them mirror images of each other.
To graph these functions, you can plot several points and then connect them with a smooth curve. You can also use a graphing calculator or online graphing tool to quickly and accurately graph the functions.
The domain of both functions is all real numbers, as there are no restrictions on the x-values. The range of f(x)=3^x is all positive real numbers, while the range of g(x)=(1/3)^x is all positive real numbers less than 1.
To determine if a graph is symmetric, you can evaluate the function for opposite x-values. If the resulting y-values are the same, then the graph is symmetric. You can also check if the function is even or odd, as even functions are symmetric about the y-axis and odd functions are symmetric about the origin.