which statement correctly describes the end behaviour of the function f(x)= x^2 - 2x + 8
To determine the end behavior of a function, we examine the values of the function as x approaches positive infinity and negative infinity.
In the given function f(x) = x^2 - 2x + 8, we can observe that it is a quadratic function.
First, let's consider x as it approaches positive infinity. As x becomes larger and larger, the x^2 term dominates the other terms. A quadratic function with a positive coefficient for the x^2 term (1 in this case) will continue to increase without bound. Therefore, as x approaches positive infinity, f(x) also approaches positive infinity.
Next, let's consider x as it approaches negative infinity. Similarly, as x becomes very negative, the x^2 term will dominate. Since the coefficient for the x^2 term is positive, the function will continue to increase without bound as x approaches negative infinity. Therefore, as x approaches negative infinity, f(x) also approaches positive infinity.
In summary, the correct statement describing the end behavior of the function f(x) = x^2 - 2x + 8 is that as x approaches positive or negative infinity, f(x) approaches positive infinity.