Exam (elaborations) College Algebra

Quiz 1 9. In the composition 𝑓(𝑔(𝑥)), the output of 𝑔 serves as
MEd 112 – College and Advanced Algebra which of the following?
First Semester, AY 2026 – 2027 A. The coefficient of function 𝑓
B. The input of function 𝑓
General Directions C. The inverse of function 𝑓
1. Strictly NO Erasures. D. The domain restriction of function 𝑓
2. Shade the letter of the best answer.
3. If the answer is not in the choices, shade E. 10. A student attempts to simplify
I. Multiple Choice 𝑥+2
Directions: Read each question carefully. Choose the 𝑥
letter of the best answer.
by canceling 𝑥 from the numerator and denominator. Why
1. What is the term used to describe the numerical factor is this procedure invalid?
of a variable term in an algebraic expression?
A. Coefficient B. Exponent A. Cancellation is allowed only when the numerator
C. Constant D. Base contains a constant.
B. Cancellation requires a common factor of the entire
2. Which of the following algebraic expressions is numerator and denominator.
classified as a monomial? C. Cancellation is never allowed when variables appear in
A. 𝑥 + 4 B. 𝑥 2 − 1 rational expressions.
𝑥+1 D. Cancellation requires the numerator and denominator
C. D. −6𝑥 2 𝑦
𝑥 to have equal degrees.

3. Which characteristic must algebraic terms possess to be 11. Which of the following relations represents a
considered like terms? function?
A. They must have equal numerical coefficients. A. {(1, 2), (2, 3), (3, 4)} B. {(1, 2), (1, 3), (2, 4)}
B. They must contain the same variables raised to the C. {(2, 1), (2, 3), (3, 5)} D. {(1, 4), (2, 5), (2, 6)}
same powers.
C. They must have the same positive or negative signs.
12. If 𝑓(𝑥) = 2𝑥 + 5, what is 𝑓(3)?
D. They must have the same total degree, regardless of
A. 8 B. 10
variables.
C. 11 D. 12
4. What is the primary purpose of factoring an algebraic
expression? 13. If 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 1, what is 𝑓(2)?
A. -3 B. -1
A. To express it as a product of simpler algebraic factors.
C. 1 D. 5
B. To convert all its variables into numerical constants. C.
To eliminate every exponent appearing in the expression.
D. To make all the terms of the expression positive. 14. A student is asked to evaluate 𝑔(𝑓(2)). Which step
must be performed first?
5. Which of the following best defines a rational algebraic A. Evaluate 𝑔(2), then substitute the result into 𝑓.
expression? B. Evaluate 𝑓(2), then substitute the result into 𝑔.
A. An expression that contains only integer coefficients. C. Multiply the values of 𝑓(2) and 𝑔(2).
B. A quotient of two polynomials with a nonzero D. Add the values of 𝑓(2) and 𝑔(2).
denominator.
C. An expression that contains at least one radical symbol. 15. Which statement best describes the mapping from
D. A polynomial whose variables have only positive Set A to Set B?
exponents.

6. Which statement correctly describes a function?
A. Each input corresponds to exactly one output.
B. Each output must correspond to exactly one input.
C. Every input must correspond to at least two outputs.
D. Every output must be different from all other outputs.
A. It is a function because every element of Set
7. What is the domain of a function? A has exactly one image in Set B.
A. The set of all possible ordered pairs. B. It is a function because element of Set B has
B. The set of all numerical coefficients. exactly one image in Set A.
C. The set of all actual output values. C. It is not a function because some elements of
D. The set of all permissible input values. Set B have no preimage.
D. It is not a function because Set A and Set B
8. What does the range of a function represent? have different numbers of elements.
A. The set of values excluded from the domain.
B. The set of all possible output values of the function.
16. Based on the mapping from Set A to Set B in no. 15,
C. The set of all actual output values of the function.
what is the range of the function?
D. The set of all variables appearing in the function.
A. {1, 2, 3} B. {𝑎, 𝑏, 𝑐, 𝑑}
C. {𝑎, 𝑐} D. {1, 𝑎, 2, 𝑐}