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Question 1A) What is a rational function?A rational function is a function where both the denominator and the numerator are polynomials. The polynomial in the rational function denominator cannot be zero.B) How is it different from a polynomial?All rational functions have two polynomial functions in it. However, not all polynomial functionsare rational functions. A rational function is a ratio of two polynomials functions. Examples of polynomial functions could be f(x)= 7x3+x2-2 and g(x)= x+5. An example of rational functions can be h(x)= f(x)/g(x). Another difference between polynomials and rational functions is that rational functions have both vertical and horizontal asymptotes.C) Provide a graph of each to demonstrate the difference.A rational function:A polynomial function:F(x)= (x2+5) / (x-3)h(x)= 2x2+4x-2
Question 2For the following functions, find:X-interceptY-interceptholesVertical asymptoteA) f(x)= (2x2-5) / (x2)Light blue answers are x-intercepts.