Question

Evaluate the function f(x) = 8x³ - 1 for values of x that approach 1 from the left and from the right.

Answer 1

The function f(x) = 8x³ - 1 approaches the value 7 as x approaches 1 from both the left and the right, because polynomial functions are continuous.

Step-by-step explanation:

To evaluate the function f(x) = 8x³ - 1 for values of x that approach 1 from the left and from the right, we can consider values of x that are slightly less than 1 (for the left-hand limit) and slightly more than 1 (for the right-hand limit). As x approaches 1 from the left, it might take on values like 0.999, while from the right it might be 1.001. However, because the function is a polynomial and thus continuous, the values of f(x) from the left and from the right will both approach the same value.

So, as x approaches 1, whether from the left or the right, we simply evaluate the function at x = 1:

f(1) = 8(1)³ - 1 = 8 - 1 = 7.

Thus, the value that f(x) approaches as x approaches 1 from either side is 7.