General Mathematics Post Test

Which of the following relation represents a function?

• {(2,1),(4,5),(6,5),(8,6)}

• {(2,4),(2,−4),(4,8),(6,2)}

• {(x,−1),(−x,−4),(x,−5),(−x,3)}

• {(−1,2),(−2,−3),(6,7),(−2,8)}

Answer explanation

The relation {(2,1),(4,5),(6,5),(8,6)} represents a function because each input (first element) is unique, ensuring that each x-value maps to exactly one y-value.

Which of the following functions define the area of a square?

• A = 3S, where s is the side of the square

• A = S^2, where s is the side of the square

• A = 2S, where s is the side of the square

• A = S^3, where s is the side of the square

Answer explanation

The area of a square is calculated using the formula A = S^2, where S is the length of a side. This means you multiply the side length by itself, making option B the correct choice.

For Sunday’s basketball tournament, Ann ordered 5 cookies for each player and 10 sandwiches for the sponsors. This can be expressed by the function f(x) = 5x+10, where x is the number of players. Which is the independent quantity in this functional relationship?

• the cookies ordered

• the number of players

• the sponsors of the game

• the number of sandwiches

Answer explanation

In the function f(x) = 5x + 10, x represents the number of players, which is the independent quantity. The number of cookies and sandwiches depend on the number of players, making them dependent variables.

• −16

• −8

• 3

• 1/2

Answer explanation

To evaluate h(x) = 8x^2 - 2x at x = -1/2, substitute -1/2 into the function: h(-1/2) = 8(-1/2)^2 - 2(-1/2) = 8(1/4) + 1 = 2 + 1 = 3. Thus, the correct answer is 3.

The following are notations for composite functions EXCEPT:

• g(f(x))

• p(h(x))

• h(x)f(x)

• (t∘s)(x)

Answer explanation

The expression h(x)f(x) represents the product of two functions, not a composite function. In contrast, g(f(x)), p(h(x)), and (t∘s)(x) all denote compositions of functions.

What do you call an inequality involving rational expression?

• Rational function

• Rational equation

• Rational inequality

• Irrational expression

Answer explanation

An inequality involving rational expressions is specifically called a 'rational inequality'. This term distinguishes it from rational functions and equations, which do not involve inequalities.

The distance from Surigao City to Butuan City is around 123 kilometers. Which of the following expresses the speed (s) as a function of travel time (t)?

• s(t) = 123/t

• s(t) = t/123

• t(s) = 123/s

• t(s) = s/123

Answer explanation

The speed (s) is calculated as distance divided by time. Given the distance of 123 kilometers, the correct formula is s(t) = 123/t, where t is the travel time. Thus, the correct choice is s(t) = 123/t.

Using the rational function g(x) = x^2−9/x−3, what is the value of g(x) when x=4? (Simplify the function first)

• 7

• −7

• 5

• −5

Answer explanation

First, simplify g(x) = (x^2 - 9)/(x - 3) = (x - 3)(x + 3)/(x - 3) = x + 3 for x ≠ 3. Then, substitute x = 4: g(4) = 4 + 3 = 7. Thus, the value of g(x) when x=4 is 7.

When the degree of the leading coefficient of the denominator is equal to the degree of the leading coefficient of the numerator, the horizontal asymptote is at y=a/b, where a and b are the leading coefficients of the numerator and denominator, respectively. The statement is ________.

• Never True

• Always True

• Sometimes True

• Cannot be determined

Answer explanation

The statement is Always True because when the degrees of the numerator and denominator are equal, the horizontal asymptote is determined by the ratio of their leading coefficients, a/b.

If the degree of the leading coefficient of the numerator is greater than to the degree of the leading coefficient of the denominator of a rational function, which of the following statements has to be true?

• The graph has no asymptote.

• The graph of the function has slant asymptote.

• The graph of the function has a horizontal asymptote.

• The graph of the function has no horizontal asymptote.

Answer explanation

When the degree of the numerator is greater than that of the denominator, the function approaches infinity as x approaches infinity, indicating that there is no horizontal asymptote.