Question

Постройте график функции: y = lg (5-x) Объясните кто-нибудь, как такое строить? Не присутствовала на данной теме.

Answer 1

Начнем с того , что  lg (5-x)=㏒₁₀ (5-x)  ОДЗ  5-x>0 ⇒ x<5  x∈(-∞;5)

y=㏒₁₀ (5-x) 

х=4      y==㏒₁₀ (5-4) ==㏒₁₀ (1) =0   т.е получили первую точку (4;0)

х= -5    у==㏒₁₀ (5-(-5)) ==㏒₁₀ (10) =1  (-5; 1)

Answer 2

Building a Graph for the Function y = lg(5-x)

To build a graph for the function y = lg(5-x), we can follow these steps:

1. Understand the Function: - The function y = lg(5-x) represents a logarithmic function with base 10, where x is the input variable.

2. Identify Key Points: - We can start by identifying key points to plot the graph. For a logarithmic function, it's important to consider the domain and range of the function.

3. Plotting the Graph: - We can plot the graph by choosing specific values for x and calculating the corresponding y values using the function y = lg(5-x). - It's also important to consider any vertical or horizontal asymptotes that may exist for the function.

4. Understanding Logarithmic Functions: - Logarithmic functions have specific characteristics, such as vertical asymptotes and transformations based on the values inside the logarithm.

5. Using Software or Calculators: - Utilizing graphing software or calculators can also help visualize the graph of the function more accurately.

Conclusion

By following these steps and understanding the characteristics of logarithmic functions, we can effectively build a graph for the function y = lg(5-x). If you have access to graphing software or a graphing calculator, it can greatly assist in visualizing the graph.