Let f(x)=x 2-x-12
(3) What power function approximates
f(x)for large x?
The square term.
what do you mean by this?
x^2-x-12. THe first term predominates as x gets large. That is what you asked.
thanks
To find the power function that approximates f(x) for large x, we need to focus on the term that dominates the behavior of the function as x approaches infinity.
Given that f(x) = x^2 - x - 12, we can see that as x becomes larger, the x^2 term will dominate the function. This means that the x^2 term will have the greatest impact on the behavior of the function for large x.
Therefore, we can approximate f(x) for large x by considering only the x^2 term.
The power function that approximates f(x) for large x would be of the form g(x) = kx^2, where k is a constant.
Hence, the power function that approximates f(x) for large x is g(x) = kx^2.