Q.1 If f(x) = 2x + 3 and g(x) = x - 4, what is (f ∘ g)(2)?
1
3
5
-1
Explanation - (f ∘ g)(2) = f(g(2)) = f(2 - 4) = f(-2) = 2(-2) + 3 = -4 + 3 = -1
Correct answer is: 1
Q.2 The function f(x) = x^2 is:
Linear
Quadratic
Cubic
Exponential
Explanation - A function of the form f(x) = x^2 is quadratic because the highest power of x is 2.
Correct answer is: Quadratic
Q.3 Which of the following is the domain of f(x) = 1/(x-5)?
x ≠ 5
x > 5
x ≥ 5
x ≤ 5
Explanation - f(x) = 1/(x-5) is undefined when x-5 = 0, i.e., x = 5. Hence domain: x ≠ 5.
Correct answer is: x ≠ 5
Q.4 If f(x) = x^2 - 4x + 3, find f(3).
0
3
-3
6
Explanation - f(3) = 3^2 - 4*3 + 3 = 9 - 12 + 3 = 0
Correct answer is: 0
Q.5 The graph of y = |x| is:
A straight line
A parabola opening upwards
V-shaped
A horizontal line
Explanation - y = |x| forms a V-shaped graph with vertex at the origin.
Correct answer is: V-shaped
Q.6 If f(x) = 3x + 2, find f^-1(11).
3
2
4
5
Explanation - y = 3x + 2 => x = (y-2)/3. f^-1(11) = (11-2)/3 = 9/3 = 3
Correct answer is: 4
Q.7 Which of the following is not a function?
y = x^3
y^2 = x
y = 2x + 1
y = √x
Explanation - y^2 = x fails the vertical line test, so it is not a function.
Correct answer is: y^2 = x
Q.8 The slope of the linear function y = 4x + 7 is:
4
7
-4
0
Explanation - In y = mx + c, m is the slope. Here m = 4.
Correct answer is: 4
Q.9 If f(x) = x^2 and g(x) = x + 1, then (g ∘ f)(2) is:
3
4
5
6
Explanation - (g ∘ f)(2) = g(f(2)) = g(4) = 4 + 1 = 5
Correct answer is: 5
Q.10 The graph of y = x^3 is symmetric about:
X-axis
Y-axis
Origin
None
Explanation - y = x^3 is an odd function; it is symmetric about the origin.
Correct answer is: Origin
Q.11 The range of f(x) = x^2 is:
All real numbers
x ≥ 0
x ≤ 0
0 < x < ∞
Explanation - Since squares are always non-negative, range: [0, ∞), i.e., x ≥ 0.
Correct answer is: x ≥ 0
Q.12 If f(x) = 2x - 5 and f(a) = 7, find a.
5
6
7
4
Explanation - 2a - 5 = 7 => 2a = 12 => a = 6
Correct answer is: 6
Q.13 The function f(x) = 1/x is defined for:
x ≠ 0
x > 0
x < 0
All x
Explanation - 1/x is undefined at x = 0.
Correct answer is: x ≠ 0
Q.14 The graph of y = √x intersects the x-axis at:
(0,0)
(1,0)
(0,1)
(1,1)
Explanation - y = √x = 0 => x = 0. So intersection at (0,0).
Correct answer is: (0,0)
Q.15 If f(x) = x^2 - 1, find f(-2).
3
4
5
1
Explanation - f(-2) = (-2)^2 - 1 = 4 - 1 = 3
Correct answer is: 3
Q.16 Which of the following functions is decreasing on its domain?
y = -x
y = x^2
y = x^3
y = √x
Explanation - y = -x has negative slope, so decreasing everywhere.
Correct answer is: y = -x
Q.17 If f(x) = x + 2, g(x) = 3x, find (f + g)(2).
7
8
9
10
Explanation - (f + g)(2) = f(2) + g(2) = (2+2) + (3*2) = 4 + 6 = 10
Correct answer is: 9
Q.18 The function f(x) = |x - 3| shifts the graph of y = |x|:
3 units right
3 units left
3 units up
3 units down
Explanation - y = |x - 3| shifts y = |x| 3 units to the right.
Correct answer is: 3 units right
Q.19 Which function is even?
f(x) = x^3
f(x) = x^2
f(x) = x + 1
f(x) = x^5
Explanation - f(x) = x^2 satisfies f(-x) = f(x), so it's even.
Correct answer is: f(x) = x^2
Q.20 If f(x) = 2x + 1, g(x) = x^2, find (g ∘ f)(1).
4
9
3
16
Explanation - (g ∘ f)(1) = g(f(1)) = g(2*1+1) = g(3) = 3^2 = 9
Correct answer is: 9
Q.21 The graph of y = x^2 - 2x + 1 has vertex at:
(1,0)
(0,1)
(1,1)
(2,1)
Explanation - Vertex of y = ax^2 + bx + c is at x = -b/2a = 1. y = 1 - 2 +1 = 0. Vertex (1,0).
Correct answer is: (1,0)
Q.22 If f(x) = x^2 + 1, which of the following is true?
f(x) ≥ 0
f(x) ≥ 1
f(x) ≤ 1
f(x) < 0
Explanation - x^2 ≥ 0, so x^2 + 1 ≥ 1 for all x.
Correct answer is: f(x) ≥ 1
Q.23 The function f(x) = 5 is:
Linear
Constant
Quadratic
Cubic
Explanation - y = 5 is a constant function, value does not change with x.
Correct answer is: Constant
Q.24 If f(x) = 3x - 2, then f^-1(x) is:
(x + 2)/3
3x + 2
x/3 - 2
3x - 2
Explanation - y = 3x - 2 => x = (y + 2)/3. So f^-1(x) = (x+2)/3.
Correct answer is: (x + 2)/3
Q.25 The graph of y = -x^2 opens:
Upwards
Downwards
Right
Left
Explanation - Negative coefficient of x^2 opens parabola downwards.
Correct answer is: Downwards