please help for this question
y1= x^-5x+6 and its reciprocal:
discuss what is the consequences for y1 to 1/y1 as x --> +- infinity?
To discuss the consequences of y1 as x approaches positive or negative infinity, we first need to simplify the given expression y1 = x^(-5x+6).
To understand the behavior of y1, we can rewrite the expression in exponential form. Recall that for any number a raised to the power of b, where b is a positive integer, a^b is equal to multiplying a by itself b number of times. Applying this to the expression, x^(-5x+6) can be written as 1 / x^(5x-6), which is the reciprocal of the original equation.
Now, let's evaluate the behavior of y1 as x approaches positive infinity, which means x becomes larger and larger. Since we have the reciprocal value of the original equation, we can evaluate the behavior of 1 / y1. As x increases towards infinity, the numerator 1 remains constant; however, the denominator x^(5x-6) grows rapidly due to the exponential term. As a result, the entire fraction 1 / y1 approaches zero, indicating that y1 itself approaches infinity as x approaches positive infinity.
On the other hand, when x approaches negative infinity, the same process applies. As x decreases towards negative infinity, the denominator x^(5x-6) still grows rapidly, but this time in negative terms. Thus, the reciprocal 1 / y1 approaches zero, indicating that y1 approaches negative infinity as x approaches negative infinity.
In summary, the consequences for y1 as x approaches positive infinity is that y1 approaches infinity, while as x approaches negative infinity, y1 approaches negative infinity.