Question

Множество значений функции y=(1/2) - 2^x

Answer 1

Множество значений функции f(x) = 2^x  (0;+∞)
Множество значений функции f(x) = -2^x (-∞;0)
Множество значений функции f(x) = (1/2) - 2^x (-∞; 1/2)

Ответ: y ∈ (-∞; 1/2)

Answer 2

Function Analysis of y=(1/2)-2^x

The function y=(1/2)-2^x represents an exponential function. Let's analyze its various aspects.

Domain and Range: The domain and range of the function y=(1/2)-2^x can be determined by analyzing the properties of exponential functions.

The domain of an exponential function is all real numbers, and the range depends on the base of the exponential function.

The function y=(1/2)-2^x is an exponential function with a base of 2. Therefore, the domain is all real numbers, and the range is all real numbers less than 1/2.

Intercepts: The function y=(1/2)-2^x has a y-intercept at (0, 1/2). To find the x-intercept, we can set y=0 and solve for x.

Behavior: Exponential functions with a base greater than 1 decrease as x increases, and those with a base between 0 and 1 decrease as x increases.

Graph: The graph of the function y=(1/2)-2^x is a decreasing exponential curve that approaches but never reaches the x-axis.

Conclusion

In conclusion, the function y=(1/2)-2^x is an exponential function with a base of 2. It has a domain of all real numbers, a range of all real numbers less than 1/2, a y-intercept at (0, 1/2), and a decreasing behavior as x increases.

Would you like to explore any other aspects of this function?