Rasmussen MAT 121 College Algebra Final
Exam 2026/2027 | 100 Verified Questions &
Answers | Instant Download
Question 1: Solve the following linear equation for x: 5x - 7 = 3x + 9
A. x = 1
B. x = 2
C. x = 4
D. x = 8
Correct Answer: D. x = 8
Rationale: To solve, first subtract 3x from both sides to get the x terms on one
side: 2x - 7 = 9. Next, add 7 to both sides to isolate the x term: 2x = 16. Finally,
divide by 2 to solve for x: x = 8. The other options are incorrect because they do
not satisfy the original equation.
Question 2: Solve the inequality for x: -3x + 5 > 14
A. x > -3
B. x < -3
C. x > 3
D. x < 3
Correct Answer: B. x < -3
Rationale: First, subtract 5 from both sides: -3x > 9. Then, divide both sides by
-3. Remember that when you divide or multiply an inequality by a negative
number, you must flip the inequality sign. This gives x < -3.
,Question 3: Find the slope of the line that passes through the points (2, 3) and
(4, 7).
A. 1/2
B. 2
C. -2
D. -1/2
Correct Answer: B. 2
Rationale: The slope formula is m = (y₂ - y₁) / (x₂ - x₁). Plugging in the points
gives m = (7 - 3) / (4 - 2) = = 2. The other options are results of miscalculating
the formula (e.g., inverting the values or misplacing a negative sign).
Question 4: Find the equation of the line with a slope of -3 that passes through
the point (1, 2).
A. y = -3x + 5
B. y = -3x - 5
C. y = 3x + 5
D. y = -3x + 2
Correct Answer: A. y = -3x + 5
Rationale: Using the point-slope form, y - y₁ = m(x - x₁), we get y - 2 = -3(x - 1).
Expanding this gives y - 2 = -3x + 3. Adding 2 to both sides results in the slope-
intercept form: y = -3x + 5.
Question 5: What is the domain of the function f(x) = √(x - 4)?
A. (-∞, 4)
B. (-∞, 4]
C. [4, ∞)
D. (4, ∞)
, Correct Answer: C. [4, ∞)
Rationale: The expression inside a square root must be non-negative.
Therefore, we set x - 4 ≥ 0. Solving for x gives x ≥ 4. In interval notation, this is [4,
∞).
Question 6: Given f(x) = x² + 2x and g(x) = 3x - 1, find (f + g)(x).
A. x² + 5x - 1
B. x² - x + 1
C. 4x² + 2x - 1
D. x² - 5x + 1
Correct Answer: A. x² + 5x - 1
Rationale: (f + g)(x) means to add the two functions: f(x) + g(x). So, (x² + 2x) +
(3x - 1) = x² + 5x - 1. The other options are incorrect combinations of the terms.
Question 7: Given f(x) = x² and g(x) = x - 3, find the composition (f ∘ g)(x).
A. x² - 3
B. x² - 6x + 9
C. x² + 6x + 9
D. x³ - 3x²
Correct Answer: B. x² - 6x + 9
Rationale: The composition (f ∘ g)(x) is defined as f(g(x)). Substitute g(x) into
f(x): f(x - 3) = (x - 3)². Expanding this binomial gives (x - 3)(x - 3) = x² - 6x + 9.
Question 8: What is the inverse of the function f(x) = (x + 3) / 2?
A. f⁻¹(x) = 2x - 3
B. f⁻¹(x) = (x - 3) / 2
, C. f⁻¹(x) = 2 / (x + 3)
D. f⁻¹(x) = 2x + 3
Correct Answer: A. f⁻¹(x) = 2x - 3
Rationale: To find the inverse, replace f(x) with y: y = (x + 3) / 2. Then swap x
and y: x = (y + 3) / 2. Solve for y: multiply by 2 to get 2x = y + 3, then subtract 3 to
get y = 2x - 3. So, f⁻¹(x) = 2x - 3.
Question 9: The graph of y = |x| is shifted 2 units to the right and 3 units down.
What is the equation of the new graph?
A. y = |x - 2| + 3
B. y = |x + 2| - 3
C. y = |x - 2| - 3
D. y = |x + 2| + 3
Correct Answer: C. y = |x - 2| - 3
Rationale: A horizontal shift to the right by h units is represented by replacing
x with (x - h), so shifting right by 2 gives |x - 2|. A vertical shift down by k units is
represented by subtracting k from the entire function, so shifting down by 3 gives
- 3. Combining these gives y = |x - 2| - 3.
Question 10: Determine if the function f(x) = x⁴ + x² is even, odd, or neither.
A. Even
B. Odd
C. Neither
D. Both
Correct Answer: A. Even
Rationale: A function is even if f(-x) = f(x). Testing this gives f(-x) = (-x)⁴ + (-x)² =
x⁴ + x², which is equal to f(x). Therefore, the function is even.
Exam 2026/2027 | 100 Verified Questions &
Answers | Instant Download
Question 1: Solve the following linear equation for x: 5x - 7 = 3x + 9
A. x = 1
B. x = 2
C. x = 4
D. x = 8
Correct Answer: D. x = 8
Rationale: To solve, first subtract 3x from both sides to get the x terms on one
side: 2x - 7 = 9. Next, add 7 to both sides to isolate the x term: 2x = 16. Finally,
divide by 2 to solve for x: x = 8. The other options are incorrect because they do
not satisfy the original equation.
Question 2: Solve the inequality for x: -3x + 5 > 14
A. x > -3
B. x < -3
C. x > 3
D. x < 3
Correct Answer: B. x < -3
Rationale: First, subtract 5 from both sides: -3x > 9. Then, divide both sides by
-3. Remember that when you divide or multiply an inequality by a negative
number, you must flip the inequality sign. This gives x < -3.
,Question 3: Find the slope of the line that passes through the points (2, 3) and
(4, 7).
A. 1/2
B. 2
C. -2
D. -1/2
Correct Answer: B. 2
Rationale: The slope formula is m = (y₂ - y₁) / (x₂ - x₁). Plugging in the points
gives m = (7 - 3) / (4 - 2) = = 2. The other options are results of miscalculating
the formula (e.g., inverting the values or misplacing a negative sign).
Question 4: Find the equation of the line with a slope of -3 that passes through
the point (1, 2).
A. y = -3x + 5
B. y = -3x - 5
C. y = 3x + 5
D. y = -3x + 2
Correct Answer: A. y = -3x + 5
Rationale: Using the point-slope form, y - y₁ = m(x - x₁), we get y - 2 = -3(x - 1).
Expanding this gives y - 2 = -3x + 3. Adding 2 to both sides results in the slope-
intercept form: y = -3x + 5.
Question 5: What is the domain of the function f(x) = √(x - 4)?
A. (-∞, 4)
B. (-∞, 4]
C. [4, ∞)
D. (4, ∞)
, Correct Answer: C. [4, ∞)
Rationale: The expression inside a square root must be non-negative.
Therefore, we set x - 4 ≥ 0. Solving for x gives x ≥ 4. In interval notation, this is [4,
∞).
Question 6: Given f(x) = x² + 2x and g(x) = 3x - 1, find (f + g)(x).
A. x² + 5x - 1
B. x² - x + 1
C. 4x² + 2x - 1
D. x² - 5x + 1
Correct Answer: A. x² + 5x - 1
Rationale: (f + g)(x) means to add the two functions: f(x) + g(x). So, (x² + 2x) +
(3x - 1) = x² + 5x - 1. The other options are incorrect combinations of the terms.
Question 7: Given f(x) = x² and g(x) = x - 3, find the composition (f ∘ g)(x).
A. x² - 3
B. x² - 6x + 9
C. x² + 6x + 9
D. x³ - 3x²
Correct Answer: B. x² - 6x + 9
Rationale: The composition (f ∘ g)(x) is defined as f(g(x)). Substitute g(x) into
f(x): f(x - 3) = (x - 3)². Expanding this binomial gives (x - 3)(x - 3) = x² - 6x + 9.
Question 8: What is the inverse of the function f(x) = (x + 3) / 2?
A. f⁻¹(x) = 2x - 3
B. f⁻¹(x) = (x - 3) / 2
, C. f⁻¹(x) = 2 / (x + 3)
D. f⁻¹(x) = 2x + 3
Correct Answer: A. f⁻¹(x) = 2x - 3
Rationale: To find the inverse, replace f(x) with y: y = (x + 3) / 2. Then swap x
and y: x = (y + 3) / 2. Solve for y: multiply by 2 to get 2x = y + 3, then subtract 3 to
get y = 2x - 3. So, f⁻¹(x) = 2x - 3.
Question 9: The graph of y = |x| is shifted 2 units to the right and 3 units down.
What is the equation of the new graph?
A. y = |x - 2| + 3
B. y = |x + 2| - 3
C. y = |x - 2| - 3
D. y = |x + 2| + 3
Correct Answer: C. y = |x - 2| - 3
Rationale: A horizontal shift to the right by h units is represented by replacing
x with (x - h), so shifting right by 2 gives |x - 2|. A vertical shift down by k units is
represented by subtracting k from the entire function, so shifting down by 3 gives
- 3. Combining these gives y = |x - 2| - 3.
Question 10: Determine if the function f(x) = x⁴ + x² is even, odd, or neither.
A. Even
B. Odd
C. Neither
D. Both
Correct Answer: A. Even
Rationale: A function is even if f(-x) = f(x). Testing this gives f(-x) = (-x)⁴ + (-x)² =
x⁴ + x², which is equal to f(x). Therefore, the function is even.
