ACCUPLACER ADVANCED ALGEBRA AND FUNCTIONS EXAM 2026/2027 PRACTICE QUESTIONS & STUDY GUIDE COMPLETE ACCURATE EXAM ACTUAL QUESTIONS AND CORRECT DETAILED SOLUTIONS WITH RATIONALES (100% CORRECT VERIFIED ANSWERS) LATEST UPDATED VERSION 2026 EDITION |G

ACCUPLACER ADVANCED ALGEBRA AND FUNCTIONS EXAM
2026/2027 PRACTICE QUESTIONS & STUDY GUIDE COMPLETE
ACCURATE EXAM ACTUAL QUESTIONS AND CORRECT DETAILED
SOLUTIONS WITH RATIONALES (100% CORRECT VERIFIED ANSWERS)
LATEST UPDATED VERSION 2026 EDITION |GUARANTEED PASS A+
(BRAND NEW!) |FULL REVISED EXAM




Question 1
If f(x)=2x2−3x+5f(x)=2x2−3x+5, find f(−2)f(−2).
A) 7
B) 15
C) 19
D) 19
Correct Answer: D
Rationale:
Substitute x=−2x=−2 into f(x)f(x): 2(4)−3(−2)+5=8+6+5=192(4)−3(−2)+5=8+6+5
=19.

Question 2
Solve for xx: 3x+1=813x+1=81.
A) 2
B) 3
C) 4
D) 5
Correct Answer: B
Rationale: 81=3481=34, so x+1=4⇒x=3x+1=4⇒x=3.

Question 3
What is the domain of f(x)=x−2x−5f(x)=x−5x−2?
A) [2,5)∪(5,∞)[2,5)∪(5,∞)

,B) (2,∞)(2,∞)
C) [2,∞)[2,∞)
D) (−∞,5)∪(5,∞)(−∞,5)∪(5,∞)
Correct Answer: A
Rationale: x−2≥0⇒x≥2x−2≥0⇒x≥2; denominator x≠5x =5. So
domain: [2,5)∪(5,∞)[2,5)∪(5,∞).

Question 4
If log⁡2(x−3)+log⁡2(x+1)=3log2(x−3)+log2(x+1)=3, find xx.
A) 3
B) 5
C) 5
D) 7
Correct Answer: C
Rationale: log⁡2((x−3)(x+1))=3⇒(x−3)(x+1)=23=8⇒x2−2x−3=8⇒x2−2x−11=0
⇒x=1±23log2
((x−3)(x+1))=3⇒(x−3)(x+1)=23=8⇒x2−2x−3=8⇒x2−2x−11=0⇒x=1±23, but
only x=5x=5 checks (since x>3x>3).

Question 5
Which function is even?
A) f(x)=x3−xf(x)=x3−x
B) f(x)=x4+2x2f(x)=x4+2x2
C) f(x)=x5−3x3f(x)=x5−3x3
D) f(x)=x3+1f(x)=x3+1
Correct Answer: B
Rationale: Even
function: f(−x)=f(x)f(−x)=f(x). (−x)4+2(−x)2=x4+2x2(−x)4+2(−x)2=x4+2x2.

Question 6
Find the inverse of f(x)=2x+1x−3f(x)=x−32x+1.
A) f−1(x)=3x+1x−2f−1(x)=x−23x+1

,B) f−1(x)=3x−1x−2f−1(x)=x−23x−1
C) f−1(x)=3x+1x+2f−1(x)=x+23x+1
D) f−1(x)=3x−1x+2f−1(x)=x+23x−1
Correct Answer: A
Rationale:
Swap xx and yy: x=2y+1y−3⇒x(y−3)=2y+1⇒xy−3x=2y+1⇒xy−2y=3x+1⇒y(x−2
)=3x+1⇒y=3x+1x−2x=y−32y+1
⇒x(y−3)=2y+1⇒xy−3x=2y+1⇒xy−2y=3x+1⇒y(x−2)=3x+1⇒y=x−23x+1.

Question 7
Simplify x2−4x2+3x+2÷x−2x+1x2+3x+2x2−4÷x+1x−2.
A) x+2x+1x+1x+2
B) x+1x+2x+2x+1
C) 1
D) x−2x−2
Correct Answer: C
Rationale: Factor: (x−2)(x+2)(x+1)(x+2)×x+1x−2=1(x+1)(x+2)(x−2)(x+2)×x−2x+1
=1.

Question 8
Solve the inequality ∣2x−1∣≤5∣2x−1∣≤5.
A) [−2,3][−2,3]
B) (−2,3)(−2,3)
C) (−∞,−2]∪[3,∞)(−∞,−2]∪[3,∞)
D) (−∞,−2)∪(3,∞)(−∞,−2)∪(3,∞)
Correct Answer: A
Rationale: −5≤2x−1≤5⇒−4≤2x≤6⇒−2≤x≤3−5≤2x−1≤5⇒−4≤2x≤6⇒−2≤x≤3.

Question 9
The graph of y=(x−2)2+3y=(x−2)2+3 is shifted 4 units left and 1 unit down. What
is the new equation?
A) y=(x+2)2+2y=(x+2)2+2

, B) y=(x−6)2+2y=(x−6)2+2
C) y=(x+2)2+2y=(x+2)2+2
D) y=(x+2)2+4y=(x+2)2+4
Correct Answer: C
Rationale: Left shift: x→x+4x→x+4 → (x+4−2)2=(x+2)2(x+4−2)2=(x+2)2; down
1: +3−1=2+3−1=2.

Question 10
If f(x)=3x−2f(x)=3x−2 and g(x)=x2+1g(x)=x2+1, find (f∘g)(2)(f∘g)(2).
A) 11
B) 13
C) 13
D) 15
Correct Answer: C
Rationale: g(2)=4+1=5g(2)=4+1=5, then f(5)=3(5)−2=13f(5)=3(5)−2=13.

Question 11
What is the vertex of y=−2x2+8x−5y=−2x2+8x−5?
A) (2,3)(2,3)
B) (−2,3)(−2,3)
C) (2,−3)(2,−3)
D) (2,3)
Correct Answer: D
Rationale:
Vertex x=−b/(2a)=−8/(2(−2))=2x=−b/(2a)=−8/(2(−2))=2, y=−2(4)+16−5=3y=−2(4
)+16−5=3.

Question 12
Solve 2x+1=x−12x+1=x−1.
A) x=0x=0 only
B) x=4x=4 only
C) x=0,4x=0,4