Question

Постройте и прочитайте график функции y=2log2x

Answer 1

Y=2log(2)x
x    1/4    1/2    1    2    4    8
y    -4      -2      0    2    4    6
D(y)∈(0;∞)
E(y)∈(-∞;∞)
ни четная и ни нечетная
несимметричная
нули функции (1;0)
возрастает на всей области определения

Answer 2

Graph of the Function y = 2log2x

To plot and read the graph of the function y = 2log2x, we need to understand the properties of logarithmic functions and how they affect the graph.

The function y = 2log2x is a logarithmic function with a base of 2. Logarithmic functions represent the inverse of exponential functions. In this case, the base 2 indicates that the function is logarithmic with respect to base 2.

The general form of a logarithmic function is y = logbx, where b is the base. In our case, b = 2. The logarithmic function y = logbx can also be written as an exponential equation: x = b^y.

To plot the graph of y = 2log2x, we can start by selecting some x-values and calculating the corresponding y-values. Let's choose x-values of 1, 2, 4, and 8:

For x = 1: y = 2log2(1) = 2 * 0 = 0

For x = 2: y = 2log2(2) = 2 * 1 = 2

For x = 4: y = 2log2(4) = 2 * 2 = 4

For x = 8: y = 2log2(8) = 2 * 3 = 6

Now, we can plot these points on a graph and connect them to visualize the function y = 2log2x.

Graph of y = 2log2x

x | y
-------
1 | 0
2 | 2
4 | 4
8 | 6

The graph of y = 2log2x will pass through these points. It is important to note that logarithmic functions have certain characteristics that affect their graphs:

1. The domain of the function y = 2log2x is all positive real numbers greater than 0. This means that x can take any value greater than 0.

2. The range of the function y = 2log2x is all real numbers. This means that y can take any real value.

3. The graph of a logarithmic function approaches but never touches the x-axis (y = 0) as x approaches positive infinity. Similarly, the graph approaches but never touches the y-axis (x = 0) as y approaches negative infinity.

4. The graph of a logarithmic function is always increasing. As x increases, y also increases.

5. The graph of a logarithmic function is symmetric with respect to the vertical line x = 1. This means that if we reflect the graph across the line x = 1, we will obtain an identical graph.

These properties can help us understand and interpret the graph of y = 2log2x.

Note: The search results provided by You.com did not contain specific information about the graph of y = 2log2x. However, the information provided above is based on the general properties of logarithmic functions and can be used to plot and interpret the graph of y = 2log2x.