Question

Построить схематично график функции y = 5 ^ |x+1|

Answer 1

1)Строим y=5^x
2)Оставляем все,что справо от оси оу и отображаем слева
3)Ось ох сдвигаем на 1 единицу вниз

Answer 2

Plotting the Function y = 5^|x + 1|

To plot the function y = 5^|x + 1|, we can start by understanding the basic shape of the function. The function involves an absolute value and an exponentiation.

The absolute value function |x + 1| ensures that the value inside the absolute value is always positive. This means that for any negative value of x, the expression |x + 1| will be equal to -(x + 1), and for any positive value of x, it will be equal to x + 1.

The exponentiation 5^|x + 1| raises the base 5 to the power of |x + 1|. This means that the value of y will be 5 raised to the power of |x + 1|.

To plot the graph, we can start by selecting some values of x and calculating the corresponding values of y. Let's choose a range of x values and calculate the corresponding y values:

| x | y = 5^|x + 1| | |---|--------------| | -3 | 5^|-3 + 1| = 5^|-2| = 5^2 = 25 | | -2 | 5^|-2 + 1| = 5^|-1| = 5^1 = 5 | | -1 | 5^|-1 + 1| = 5^|0| = 5^0 = 1 | | 0 | 5^|0 + 1| = 5^|1| = 5^1 = 5 | | 1 | 5^|1 + 1| = 5^|2| = 5^2 = 25 | | 2 | 5^|2 + 1| = 5^|3| = 5^3 = 125 | | 3 | 5^|3 + 1| = 5^|4| = 5^4 = 625 |

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


The graph of the function y = 5^|x + 1| is a curve that starts at (0, 1), increases as x moves away from 0, and becomes steeper as x increases or decreases. The graph is symmetric with respect to the y-axis.

Please note that the graph is an approximation and may not be perfectly accurate. It is always a good idea to use graphing software or a graphing calculator for precise plotting.

I hope this helps! Let me know if you have any further questions.