mathematics beginner 10 sample questions

Algebra Functions MCQ Practice Test

Input-output relationships and mapping

Q1. A function f(x) is defined as f(x) = 2x + 1. What is the value of f(3) + f(-2)?

A. f(3) + f(-2) = 10
B. f(3) + f(-2) = 6
C. f(3) + f(-2) = 8
D. f(3) + f(-2) = 4 ✓

Explanation: f(3) = 2(3) + 1 = 7 and f(-2) = 2(-2) + 1 = -3, so f(3) + f(-2) = 7 + (-3) = 4.

Q2. The function f(x) = 2x + 5 is reflected in the y-axis. What is the equation of the reflected function?

A. f(x) = -2x - 5
B. f(x) = 2x - 5
C. f(x) = -2x + 5 ✓
D. f(x) = 2x + 10

Explanation: When a function is reflected in the y-axis, the x term is negated. So, the equation of the reflected function is f(x) = -2x - 5.

Q3. Solve for y in the equation y = −2x + 5, given that x is 3.

A. y = −2
B. y = 1
C. y = −1 ✓
D. y = 7

Explanation: Substituting x = 3 into y = -2x + 5: y = -2(3) + 5 = -6 + 5 = -1.

Q4. A function f(x) is defined as f(x) = 2x + 1. If the function is shifted 3 units to the left, what is the new function f(x)?

A. f(x) = 2(x - 3) + 1
B. f(x) = 2x + 4
C. f(x) = 2(x + 3) + 1 ✓
D. f(x) = 2x - 1

Explanation: Shifting a graph 3 units left replaces x with (x + 3): g(x) = f(x + 3) = 2(x + 3) + 1 = 2x + 7. The old key, 2(x − 3) + 1, is the shift to the RIGHT, and the old explanation even derived (x + 3) before contradicting itself.

Q5. What is the value of f(-2) for the function f(x) = 2x^2 + 5x - 3?

A. f(-2) = -5 ✓
B. f(-2) = 5
C. f(-2) = -11
D. f(-2) = -1

Explanation: Substituting x = -2: f(-2) = 2(-2)^2 + 5(-2) - 3 = 2(4) - 10 - 3 = 8 - 10 - 3 = -5. The old key was a meta-sentence admitting -5 was missing from the options, and the old explanation looped endlessly without committing.

Q6. The function f(x) = 2x + 5 is reflected across the y-axis. What is the equation of the new function after reflection?

A. f(-x) = -2x - 5
B. f(-x) = 2x - 5
C. f(-x) = -2x + 5 ✓
D. f(-x) = 2x + 5

Explanation: When a function is reflected across the y-axis, the x term is negated. Therefore, f(-x) = 2(-x) + 5 = -2x + 5 is the equation of the new function.

Q7. A function f(x) is defined as f(x) = 2x^2 + 5x - 3. What is the value of f(-1)?

A. f(-1) = -8
B. f(-1) = -7
C. f(-1) = -6 ✓
D. f(-1) = -5

Explanation: To find the value of f(-1), substitute x = -1 into the function f(x) = 2x^2 + 5x - 3. This gives f(-1) = 2(-1)^2 + 5(-1) - 3 = 2(1) - 5 - 3 = 2 - 5 - 3 = -6.

Q8. What is the value of f(-1) for the function f(x) = 2x^2 + 5x - 3?

A. f(-1) = -6 ✓
B. f(-1) = 6
C. f(-1) = -4
D. f(-1) = 0

Explanation: Substituting x = -1: f(-1) = 2(-1)^2 + 5(-1) - 3 = 2(1) - 5 - 3 = 2 - 5 - 3 = -6. The old options omitted -6 and the old explanation spun in circles computing it without ever correcting the key.

Q9. Which of the following functions satisfies f(3) = 11?

A. f(x) = 2x + 1
B. f(x) = 2x + 5 ✓
C. f(x) = x + 5
D. f(x) = 3x - 1

Explanation: Substituting x = 3: f(x) = 2x + 5 gives 2(3) + 5 = 11, so it is the function satisfying the condition. The distractors give 7, 8, and 8 respectively. The original stem asked to "find x" while the options were functions, so it was reworded to ask for the function.

Q10. If f(x) = 2x^2 + 3x - 1 and g(x) = x^2 - 2x + 1, what is the value of (f ∗ g)(2)?

A. (f ∗ g)(2) = 2(2^2 + 3(2) - 1)(2^2 - 2(2) + 1)
B. (f ∗ g)(2) = (2(2)^2 + 3(2) - 1)(2^2 - 2(2) + 1) ✓
C. (f ∗ g)(2) = 2(2^2) + 3(2) - 1 × (2^2 - 2(2) + 1)
D. (f ∗ g)(2) = 2(2^2 + 3(2) - 1) + (2^2 - 2(2) + 1)

Explanation: To find the value of (f ∗ g)(2), we need to multiply the two functions f(x) and g(x) at x = 2. This means we need to substitute x = 2 into both functions and then multiply the results. The correct expression for (f ∗ g)(2) is obtained by multiplying the two expressions for f(2) and g(2).

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