Let f(x) = 1/x
Evaluate and plot g(x)= -f(2x) + 1
Start with the innermost transformation and work outward in steps. There are 3 transformations
To evaluate and plot the function g(x) = -f(2x) + 1, we need to apply three transformations step by step.
Transformation 1: Applying the innermost transformation
Start with the innermost transformation, which is f(2x).
The function f(x) = 1/x is a rational function that gives us the reciprocal of any given input value. To apply the transformation f(2x), we need to replace x with (2x) in the original function:
f(2x) = 1/(2x)
Transformation 2: Applying the next transformation, -f(2x)
Next, we need to apply the transformation -f(2x) on the result of the previous transformation.
-g(2x) = -(1/(2x))
Transformation 3: Applying the final transformation, -f(2x) + 1
Lastly, we need to add 1 to the result of the previous transformation:
g(x) = -f(2x) + 1 = -(1/(2x)) + 1
Now, we have the final expression for g(x). To evaluate and plot this function, we can follow these steps:
1. Choose a range of x values that you want to evaluate the function over. For example, let's choose x values between -10 and 10.
2. Plug in each value of x into the expression for g(x). For each x value, calculate the corresponding y value.
3. Create a table of the x and y values you calculated.
4. Plot the x and y values on a coordinate plane. The x values will be on the horizontal axis, and the y values will be on the vertical axis.
5. Connect the plotted points with a smooth curve to represent the graph of g(x).
Note: When evaluating the function, pay attention to any specific restrictions, such as division by zero, which could result in undefined values. In this case, since f(x) = 1/x, we cannot have x = 0. Make sure to exclude this value from the range of x values you choose.