Question

th fu + + + + X + + 1-2 f(x) = {0 2 if x < 0 if x = 0 if x > 0 50. the graph of y = f(x) is shown above, which of the following statements must be true? I. f(x) > 0 II. f(x) = -f(-x) III. If x < x2, then f(x) = f(x2) (A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

Answer 1

solution : I. If all >o y=ffcall y (see graph) of fast Take the mirror image of in x-axi. in x-axis) of the portion of the graph of f(n) which lies below x-axis, 34 4 -3 -2 -! 2 3 4 from the graph of Ifall we observe that Ifa) 70 so, If (ny) so is false. I. fal= -fr-n). To draw ful = -fl: a) take image of fun about y-axis to obtain frong and then take image of for about x-axis to obtain -fen). -3 -2 -1

falz -ffn It is trul. Hence, IT If nine then flai) = f(12) It is true because function is increasing function. Hence, ( I and I only Answer.