Mathematics 1

Yanıt Açıklaması: vertex = (h, k) ; h =- b / 2a for y = a x 2 + b x + c ; k = 9 – 18 + 4 = -5 . pg. 60. Correct answer is C.

Yanıt Açıklaması: A={2, 4, 6, 7}, B={1, 2, 3, 4} and C={8, 7,4}. AUB={1,2,3,4,6,7} and AUBUC={1,2,3,4,6,7,8}. The answer is B.

Yanıt Açıklaması: x 2 -5x+6=(x-2)(x-3)=0 So either x-2=0 or x-3=0 could satisfy this equation. If x-2=0, then x=2 and if x-3=0, then x=3. Thus the solution set is (2,3)

Yanıt Açıklaması:

Yanıt Açıklaması: x = 3 1/2 = 1.732.... . Correct answer is E.

Yanıt Açıklaması: A ∪ B = {1, 2, 3, 4, 5}, A ∩ B = {3}, A \ B = {1, 2}, B \ A = {4,5}, A c = {5, 6, 7, 8, 9, 10}, B c = {1, 2, 6, 7, 8, 9, 10}.

Yanıt Açıklaması: By using the graph which is given in the question; f(-5)=1, f(-4)=8, f(3)=-6 and f(5)=6 then, f(-4)+3f(5)-2f(3)=8+(3.6)-(2.-6)=8+18-(-12)=38

Yanıt Açıklaması: f(x)=2x+7 and g(x)=3x-2 ›(gof)(x)=3.(2x+7)-2=6x+21-2=6x-19

Yanıt Açıklaması: f(x)=3x-8 › f(3)=3.3-8=1 g(x)=(x+12)/4 › g(8)=(8+12)/4=20/4=5 f(3).g(8)=1.5=5

Yanıt Açıklaması: c = log 2 (5 / 10) = log 2 2 -1 ; log 2 c = 2 -1 ; 3 = 9 1/2 ; x = 2 -1 1/2 = 2 -2 = 0.25 . Correct answer is A.

Yanıt Açıklaması: x = 2 + 3 x 3 – x + 1 = 1 . Correct answer is D.

Yanıt Açıklaması: Consider the function f : . For every x 1 , x 2 A if x 1 ? x 2 implies f ( x 1 ) ? f ( x 2 ) then the function f is called one-to-one (or injective), so the correct answer is A. Although the range and the image of a function are two concepts that need to be distinguished, we still know that they are closely related. The image is always a subset of the range. Yet, there are functions for which the range and the image sets are exactly the same. Thus, given a function f : if the image is equal to the range, i.e. f ( A )= B the function f is called surjective (onto). Equivalently, for every element b of the set B if there can be found an element a of A such that f ( a )= b , then f is called onto. If a function which is both one-to-one and onto is called a bijection. Constant function and identity function are the concepts related to types of functions. A function assigning each element from its domain a single element in its range is called a constant function. Given A ? , a function defined on the set A and assigning every element of A to itself is called the identity function.

Yanıt Açıklaması: Consider the function that assigns to each real number three times itself and four. If we denote this real number by x, and the function by f we may express it as It is customary to also denote this function by y = f ( x ). In the expression y = f ( x ), x is called the independent variable, whereas y is called the dependent variable. In the expression y is called the dependent variable. In the equation y = f ( x )=3 x +4, the dependent variable y is a function of the independent variable x . As also understood from the information given, the correct answer is E. All of the statements in the options are correct.

Yanıt Açıklaması: 3 2 =9 3 -2 =1/9 So, (3 2 -3 -2 )/(3 2 +3 -2 )=(9-1/9)/(9+1/9)=(80/9)/(82/9)=80/82

Yanıt Açıklaması: (4f –2g)(x) = 4(x-2) - 2(2x-9) = 4x - 8 - 4x + 18 = 10

Yanıt Açıklaması: I. x with degree is 1. II. 3x+ 1 with degree is 1. III. 1 with degree is 0. Therefore the answer is A.

Yanıt Açıklaması: Substituting 3 for x we find f (3) = 5.3 - 4 = 15 – 4 = 11, so the correct answer is A.