The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x)=f(x)g(x) and v(x)=f(x)/g(x) Find each of the following:u(x) and v(x)..
Well, u(x) is a combination of f(x) and g(x), so it's kind of like when Batman and Robin team up - they become a dynamic duo. u(x) is like the Batman-Robin of functions. It takes the qualities of both f(x) and g(x) and multiplies them together. It's a true power couple.
On the other hand, v(x) is like a love-hate relationship. It's the f(x)/g(x) quotient. It's kind of like when you're at a dinner party and you have to divide a single piece of cake among all your friends - it creates a lot of tension. In this case, f(x) and g(x) are having a bit of a disagreement, and v(x) is the result of that division.
So, in summary, u(x) is the tag-team champions of functions, while v(x) is the result of a divided partnership.
To find u(x), we need to multiply the functions f(x) and g(x). Looking at the graph, we can see that f(x) is the blue curve and g(x) is the red curve.
To find the product of two functions, we multiply their values at each x-coordinate. So, for each x, u(x) = f(x) * g(x).
To find v(x), we need to divide the function f(x) by g(x). So, for each x, v(x) = f(x) / g(x).
To find the values of u(x) and v(x) at specific x-coordinates, we need to read off the corresponding points from the graph.
To find the function u(x), which is the product of f(x) and g(x), follow these steps:
1. Look at the graph and find the value of f(x) at each x-coordinate.
2. Look at the graph and find the value of g(x) at each x-coordinate.
3. Multiply the corresponding values of f(x) and g(x) for each x-coordinate to get the value of u(x).
To find the function v(x), which is the quotient of f(x) divided by g(x), follow these steps:
1. Look at the graph and find the value of f(x) at each x-coordinate.
2. Look at the graph and find the value of g(x) at each x-coordinate.
3. Divide the corresponding values of f(x) by g(x) for each x-coordinate to get the value of v(x).
Note: It is important to ensure that g(x) is not zero at any x-coordinate since division by zero is undefined.
Unfortunately, since there is no graph provided, I am unable to provide you with the specific values of u(x) and v(x). However, by following the steps outlined above and using the given graphs, you should be able to calculate u(x) and v(x) yourself.