Question

Исследовать и построить график функции y= -5/x+1

Answer 1

У-5х=1
у^2-13х=23
y=5x+1
(5x+1)^2-13x=23
25x^2+10x+1-13x-23=0
25x^2-3x-22=0
D=47
x=1
y=5*1+1=6

Answer 2

Function and Graph Analysis

The given function is y = -5/x + 1. Let's analyze and plot the graph of this function.

To plot the graph, we need to determine the behavior of the function for different values of x. By observing the function, we can see that it is a rational function with a vertical asymptote at x = 0. This means that the function approaches positive or negative infinity as x approaches 0 from the left or right, respectively.

To find the x-intercept, we set y = 0 and solve for x:

0 = -5/x + 1

Rearranging the equation, we get:

5/x = 1

Cross-multiplying, we have:

x = 5

So the x-intercept is x = 5.

To find the y-intercept, we set x = 0 and solve for y:

y = -5/0 + 1

Since division by zero is undefined, the function does not have a y-intercept.

Now, let's plot the graph of the function.

Graph of y = -5/x + 1

To plot the graph, we can use a table of values or a graphing calculator. Here is a table of values for the function:

| x | y | |-----|-------------| | -5 | -1.2 | | -4 | -1.25 | | -3 | -1.33 | | -2 | -1.5 | | -1 | -6 | | 1 | -4 | | 2 | -3.5 | | 3 | -3.33 | | 4 | -3.25 | | 5 | -3.2 |

Now, let's plot these points on a graph:


Note: The graph is not defined at x = 0 due to the vertical asymptote.

Conclusion

In conclusion, the function y = -5/x + 1 is a rational function with a vertical asymptote at x = 0. It has an x-intercept at x = 5 and does not have a y-intercept. The graph of the function exhibits a hyperbolic shape.