Cracking the SAT Subject Test in Math 2, 2nd Edition 48 Which of the following lines is an asymptote of the graph of ? I x = 2 II y = − III y = −1 (A) I only (B) II only (C) III only (D) I and II only[.]
48 Which of the following lines is an asymptote of the graph of ? I x = 2 II y = − III y = −1 (A) I only (B) II only (C) III only (D) I and II only (E) I and III only ROOTS OF FUNCTIONS IN GRAPHS The roots of a function are the values that make the function equal to zero Hence, the roots are also called zeros or solutions of the function To find the roots of a function f(x) algebraically, you simply set f(x) equal to zero and solve for x The values of x that you find are the roots of the function Graphically, the roots of a function are the values of x at which the graph crosses the x-axis, that is, the x-intercepts That makes them easy to spot on a graph If you are asked to match a function to its graph, it’s often helpful to find the roots of the function using algebra; then it’s a simple matter to compare the function’s roots to the x-intercepts on the graph Take a look at this function: f(x) = x3 + 3x2 − 4x If you factor it to find its roots, you get: f(x) = x(x + 4)(x − 1) The roots of f(x) are therefore x = −4, 0, and 1 You can expect the graph of y = f(x) to cross the x-axis at those three x-values On the SAT Subject Test in Math 2, you may be asked to find the roots of a nasty-looking function Luckily the test is multiple choice, so you can Plug In The Answers on those problems Simply plug each answer choice into the function and find the answer which makes the function equal zero Remember that ETS rounds, so an answer choice that is very close to zero is likely to be correct DRILL 8: ROOTS OF FUNCTIONS Try the following practice questions by working with the roots of functions The answers can be found in Part IV 16 Which of the following is a zero of f(x) = 2x2 − 7x + 5 ? (A) 1.09 (B) 1.33 (C) 1.75 (D) 2.50 (E) 2.75 19 The function g(x) =x3 + x2 − 6x has how many distinct roots? (A) (B) (C) (D) (E) It cannot be determined from the information given .. .The roots of f(x) are therefore x = −4, 0, and 1 You can expect the graph of y = f(x) to cross the x-axis at those three x-values On the SAT Subject Test in Math 2, you may be asked to find the roots of... nasty-looking function Luckily the test is multiple choice, so you can Plug In The Answers on those problems Simply plug each answer choice into the function and find the answer which makes the function... DRILL 8: ROOTS OF FUNCTIONS Try the following practice questions by working with the roots of functions The answers can be found in Part IV 16 Which of the following is a zero of f(x) = 2x2 − 7x + 5 ?