Q.1 What is the domain of the function f(x) = 1/x?
All real numbers
All real numbers except 0
x > 0
x < 0
Explanation - The function f(x) = 1/x is undefined at x = 0, so the domain excludes 0.
Correct answer is: All real numbers except 0
Q.2 If f(x) = 2x + 3, what is f(4)?
8
10
11
12
Explanation - Substituting x = 4: f(4) = 2(4) + 3 = 11.
Correct answer is: 11
Q.3 Which of the following is a quadratic function?
f(x) = x + 2
f(x) = x^2 + 3x + 1
f(x) = 1/x
f(x) = √x
Explanation - A quadratic function is a polynomial of degree 2, so f(x) = x^2 + 3x + 1 fits the definition.
Correct answer is: f(x) = x^2 + 3x + 1
Q.4 If f(x) = x^2 and g(x) = x + 1, what is (f ∘ g)(2)?
3
4
9
16
Explanation - (f ∘ g)(2) = f(g(2)) = f(3) = 3^2 = 9.
Correct answer is: 9
Q.5 The graph of y = f(x) = x^2 is symmetric about which axis?
x-axis
y-axis
y = x
origin
Explanation - The parabola y = x^2 is symmetric about the y-axis.
Correct answer is: y-axis
Q.6 If f(x) = 2x - 5, what value of x makes f(x) = 9?
2
5
6
7
Explanation - Solve 2x - 5 = 9 → 2x = 14 → x = 7.
Correct answer is: 7
Q.7 The range of f(x) = x^2 for real numbers is:
All real numbers
x ≥ 0
x > 0
x ≤ 0
Explanation - Squaring any real number yields a non-negative result, so the range is x ≥ 0.
Correct answer is: x ≥ 0
Q.8 Which of the following is NOT a function?
y = x^2
y = |x|
x = y^2
y = 3x + 1
Explanation - x = y^2 fails the vertical line test since for each x there can be two values of y.
Correct answer is: x = y^2
Q.9 If f(x) = 3x and g(x) = x + 2, what is (f ∘ g)(x)?
3x + 2
3x + 6
3x - 2
3x^2 + 2
Explanation - (f ∘ g)(x) = f(g(x)) = f(x+2) = 3(x+2) = 3x + 6.
Correct answer is: 3x + 6
Q.10 The function f(x) = √(x-1) is defined for:
x > 1
x ≥ 1
x < 1
All real x
Explanation - The square root requires a non-negative input, so x - 1 ≥ 0 → x ≥ 1.
Correct answer is: x ≥ 1
Q.11 If f(x) = x^2 - 4, what are the zeros of f(x)?
±2
±4
0 and 4
0 and -4
Explanation - Solve x^2 - 4 = 0 → x^2 = 4 → x = ±2.
Correct answer is: ±2
Q.12 If f(x) = 2x^2 and g(x) = x + 3, what is (g ∘ f)(2)?
5
7
11
11
Explanation - (g ∘ f)(2) = g(f(2)) = g(8) = 8 + 3 = 11.
Correct answer is: 11
Q.13 Which of these functions is linear?
f(x) = x^2 + 1
f(x) = 3x - 7
f(x) = √x
f(x) = 1/x
Explanation - A linear function has the form f(x) = mx + b, which matches f(x) = 3x - 7.
Correct answer is: f(x) = 3x - 7
Q.14 If f(x) = x^3, what is f(-2)?
-6
-8
6
8
Explanation - f(-2) = (-2)^3 = -8.
Correct answer is: -8
Q.15 Which of the following is the inverse of f(x) = 2x + 1?
f⁻¹(x) = x/2 + 1
f⁻¹(x) = (x - 1)/2
f⁻¹(x) = 2x - 1
f⁻¹(x) = x - 2
Explanation - To find the inverse, swap x and y: y = 2x + 1 → x = 2y + 1 → y = (x - 1)/2.
Correct answer is: f⁻¹(x) = (x - 1)/2
Q.16 If f(x) = |x|, what is f(-5)?
-5
0
5
Undefined
Explanation - Absolute value makes all inputs non-negative, so f(-5) = 5.
Correct answer is: 5
Q.17 The graph of f(x) = -x^2 opens:
Upward
Downward
Sideways
Not a parabola
Explanation - The negative coefficient of x^2 makes the parabola open downward.
Correct answer is: Downward
Q.18 If f(x) = 3x + 2, what is f⁻¹(x)?
(x - 2)/3
(x + 2)/3
3x - 2
1/(3x + 2)
Explanation - To find the inverse: y = 3x + 2 → x = 3y + 2 → y = (x - 2)/3.
Correct answer is: (x - 2)/3
Q.19 If f(x) = 2x, what is f(f(x))?
2x
4x
x^2
2x^2
Explanation - f(f(x)) = f(2x) = 2(2x) = 4x.
Correct answer is: 4x
Q.20 The vertex of y = (x - 2)^2 + 3 is:
(0,0)
(2,3)
(-2,3)
(3,2)
Explanation - The vertex form y = (x-h)^2 + k has vertex (h,k), so (2,3).
Correct answer is: (2,3)
Q.21 If f(x) = 1/x, what is f(1/2)?
1/2
2
-2
0
Explanation - f(1/2) = 1/(1/2) = 2.
Correct answer is: 2
Q.22 The graph of f(x) = |x| has shape of:
Parabola
V-shape
Straight line
Circle
Explanation - Absolute value functions graph into a V-shape.
Correct answer is: V-shape
Q.23 If f(x) = x^2 + 2x + 1, what is f(-1)?
0
1
2
3
Explanation - f(-1) = (-1)^2 + 2(-1) + 1 = 1 - 2 + 1 = 0.
Correct answer is: 0
Q.24 If f(x) = x^2 and g(x) = √x, what is (f ∘ g)(9)?
3
9
81
Undefined
Explanation - (f ∘ g)(9) = f(g(9)) = f(√9) = f(3) = 9.
Correct answer is: 9