Question 217·Easy·Nonlinear Functions
What is ?
For questions asking for a function value like , the fastest method is usually to substitute directly into the given formula, using parentheses to keep signs straight. If the function is a rational expression, check whether the numerator factors and simplifies with the denominator first, as this can turn a tricky fraction into a simple linear expression—just be sure the substitution point does not make the denominator zero. Always double-check signs in both the numerator and the denominator to avoid turning a negative answer into a positive one or vice versa.
Hints
Start by substituting
Try directly plugging into both the numerator and the denominator . Be careful with negative signs and parentheses.
Simplify the numerator
Before substituting, see if you can factor . Recognizing a common pattern might make the function simpler.
Cancel common factors (but watch the domain)
After factoring the numerator, see if there is a common factor with the denominator that you can cancel, and then plug in to the simplified expression.
Desmos Guide
Enter the function
In Desmos, type f(x) = (x^2 - 4x + 4)/(x - 2) to define the function.
Evaluate at x = -2
In a new line, type f(-2) and look at the numeric output that Desmos gives; that number is the value of .
Step-by-step Explanation
Understand and, if you like, simplify the function
The function is
Notice the numerator is a perfect square trinomial:
So, for ,
This simpler form is easier to plug into.
Evaluate the simplified expression at x = -2
Using the simplified form (which is valid for ), substitute :
Now compute this difference.
Compute the final value
Evaluate the expression from the previous step:
So , which corresponds to answer choice B.