use the asymptotes and intercepts to make a quick sketch of the function f(x)= x-2 (numerator) x+4(denominator) and its reciprocal f^r = x+4 (numerator) x-2 (denominator) on the same set of axes.
b) describe the symmetry in the graphs in part a)
c) determine the intervals of increase and decrease for both f and f^r, how do the sets of intervals compare?
d) would the pattern occur for all pairs of functions f(x)= x+b (numerator) x+d and f^r(x) = x+d (numerator)and x+b (denominator)? explain why or why not?
REINY OR WHOEVER IS READING THIS, I JUST NEED TO KNOW THE ANSWER FOR D
To answer part (d) of your question, let's analyze the pattern in the pairs of functions and determine if it occurs for all pairs of functions of the form f(x) = x + b (numerator) and f^r(x) = x + d (numerator) and x + b (denominator).
In the given original pair of functions f(x) = x - 2 (numerator) / x + 4 (denominator) and f^r(x) = x + 4 (numerator) / x - 2 (denominator), we can see a specific pattern.
The numerator and denominator of the original function f(x) = x - 2 / x + 4 are swapped to create the reciprocal function f^r(x) = x + 4 / x - 2.
Let's test this pattern with another pair of functions.
Consider f(x) = x + b (numerator) / x + d (denominator) and f^r(x) = x + d (numerator) / x + b (denominator), where b and d are any real numbers.
If we swap the numerator and denominator of the original function f(x) = x + b (numerator) / x + d (denominator), we get f^r(x) = x + d (numerator) / x + b (denominator).
This pattern holds true for any values of b and d. Therefore, the pattern occurs for all pairs of functions of the given form.
In conclusion, when the numerator and denominator are swapped, the reciprocal function can be obtained, and this pattern holds for all pairs of functions f(x) = x + b (numerator) / x + d (denominator) and f^r(x) = x + d (numerator) / x + b (denominator).