Mathematics Function and Relation Quiz

Fill in each blank so that the resulting statement is true. If the x-intercepts of a function are -10 and -3, then f(-10) = _______ and f(-3) = _______. The x-intercepts, -10 and -3, are called the _______ of the function. If the x-intercepts of a function are -10 and -3, then f(-10) = (1) _______ and f(-3) = (2) _______. The x-intercepts, -10 and -3, are called the (3) _______ of the function.

• 0, 0, zeros

• -10, -3, roots

• 1, 1, solutions

• -3, -10, factors

What is a relation? Describe what is meant by its domain and its range. Choose the correct answer below.

• A relation is any set of ordered pairs. The set of all second components of the ordered pairs is called the domain of the relation and the set of all first components is called the range of the relation.

• A relation is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range.

• A relation is a correspondence from a second set, called the domain, to a first set, called the range, such that each element in the domain corresponds to exactly one element in the range.

• A relation is any set of ordered pairs. The set of all first components of the ordered pairs is called the domain of the relation and the set of all second components is called the range of the relation.

Does f(x) mean f times x when referring to function f? If not, what does f(x) mean? Provide an example with your explanation. Choose the correct answer below.

• The notation f(x) means f times x when referring to function f.

• The notation f(x) does not mean f times x. The notation f(x) describes the value of the function at x. For example, f(3) = 10 means that the value of the function f at 3 is 10.

• The notation f(x) does not mean f times x. The notation f(x) describes f parts of x. For example, f(3) means f parts of 3.

• The notation f(x) does not mean f times x. The notation f(x) describes the value of the function at -x. For example, f(3) = 10 means that the value of the function at -3 is 10.

Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points (-4, -2) and (4,7).

• The slope of the parallel line is 9/8.

• The slope of the parallel line is undefined.

• The slope of the perpendicular line is -8/9.

• The slope of the parallel line is 1.

Select the answers that best complete the given statement. The notation f o g, called the (1) ______ of the function f with g, is defined by (f o g)(x) = (2) ______.

• (1) inverse, (2) g(f(x)).

• (1) composition, (2) g(f(x)).

• (1) inverse, (2) f(g(x)).

• (1) composition, (2) f(g(x)).

Determine whether the following statement makes sense or does not make sense, and explain your reasoning. A student found the inverse of f(x) = 6x - 3 mentally by reversing "multiplying by 6 and subtracting 3" to get "adding 3 and dividing by 6," so f⁻¹(x) = x + 3/6.

• The statement does not make sense because f⁻¹(x) = (x + 3)/6.

• The statement does not make sense because f⁻¹(x) = 6/(x + 3).

• The statement makes sense because f⁻¹(x) = (x + 3)/6.

• The statement makes sense because f⁻¹(x) = 6x + 3.

Determine whether the following statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inverse of {(4,5),(5,6)} is {(5,6),(4,5)}.

• The statement is true.

• The statement is false. The correct statement is the inverse of {(4,5),(5,6)} is {(5,4),(6,5)}.

• The statement is false. The correct statement is the inverse of {(4,5),(5,6)} is {(5,5),(6,4)}.

• The statement is false. The correct statement is the inverse of {(4,5),(5,6)} is {(6,5),(5,4)}.

The function P(x) = 0.6x - 54 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes. Find P(900), the profit the vendor makes from selling 900 pretzels.

Fill in the blanks in the sentence below so that the resulting statement is true. The slope-intercept form of the equation of a line is (1) __________, where m represents the (2) __________ and b represents the (3) __________.

• (1) y = mx + b, (2) slope, (3) y-intercept

• (1) y = bx + m, (2) y-intercept, (3) slope

• (1) y = mx + b, (2) y-intercept, (3) slope

• (1) y = bx + m, (2) slope, (3) y-intercept

Determine the slope and the y-intercept of the graph of the equation. 5x – 6y – 30 = 0

• m = 5; (0,30)