PRECALCULUS 10TH EDITION BY RON LARSON EXAM
2026/2027 | COMPLETE QUESTIONS AND ANSWERS
(VERIFIED ANSWERS) | EXAM PREP | LATEST EXAM
GUIDE 2026&2027
1. Which statement best describes the domain of the function f(x) = √(x − 4)?
A. x < 4
B. x ≤ 4
C. x ≥ 4
D. All real numbers
For a square-root function, the expression inside the radical must be nonnegative. Thus x − 4 ≥
0, giving x ≥ 4.
2. If f(x) = 3x − 7, what is f(5)?
A. 8
B. 15
C. 22
D. −8
Substituting x = 5 gives f(5) = 3(5) − 7 = 15 − 7 = 8.
3. Which equation represents a line with slope 4 and y-intercept −3?
A. y = −3x + 4
B. y = 4x − 3
C. y = 3x − 4
D. y = −4x − 3
Slope-intercept form is y = mx + b. With m = 4 and b = −3, the equation is y = 4x − 3.
4. A line passes through (2, 5) and (6, 13). What is its slope?
A. 1
B. 2
C. 3
D. 4
The slope is (13 − 5)/(6 − 2) = 8/4 = 2.
5. Which function is even?
,A. f(x) = x³ + x
B. f(x) = x² + 4
C. f(x) = x³ − 2
D. f(x) = x² + x
A function is even when f(−x) = f(x). For x² + 4, replacing x with −x produces the same
expression.
6. If f(x) = x² − 2x + 1, which form most clearly identifies the vertex?
A. (x − 1)²
B. (x + 1)²
C. x² − 2x
D. (x − 1)² + 1
Completing the square gives x² − 2x + 1 = (x − 1)², so the vertex is (1, 0).
7. What is the inverse of f(x) = 2x + 5?
A. f⁻¹(x) = 2x − 5
B. f⁻¹(x) = (x + 5)/2
C. f⁻¹(x) = (x − 5)/2
D. f⁻¹(x) = 5x − 2
Set y = 2x + 5, interchange x and y, and solve: x = 2y + 5, so y = (x − 5)/2.
8. If f(x) = x + 2 and g(x) = x², what is (g ∘ f)(3)?
A. 9
B. 11
C. 25
D. 15
First calculate f(3) = 5. Then apply g: g(5) = 25.
9. Which transformation changes f(x) into f(x − 6)?
A. Shift left 6 units
B. Shift right 6 units
C. Shift up 6 units
D. Shift down 6 units
Replacing x with x − 6 shifts the graph horizontally 6 units to the right.
10. What is the x-intercept of y = 2x − 10?
,A. −5
B. 2
C. 5
D. 10
At the x-intercept, y = 0. Therefore 0 = 2x − 10, giving x = 5.
11. Which expression is equivalent to (x² − 9)/(x − 3), where x ≠ 3?
A. x − 3
B. x + 3
C. x² + 3
D. x² − 6
Since x² − 9 = (x − 3)(x + 3), cancellation gives x + 3 for x ≠ 3.
12. What is the domain of f(x) = 1/(x + 7)?
A. x ≠ −7
B. x ≠ 7
C. x > −7
D. All real numbers
The denominator cannot equal zero. Therefore x + 7 ≠ 0, so x ≠ −7.
13. Which equation is equivalent to 2x + 3y = 12 in slope-intercept form?
A. y = 2x + 4
B. y = −2/3x + 4
C. y = 2/3x − 4
D. y = −3/2x + 12
Solving for y gives 3y = −2x + 12 and therefore y = −(2/3)x + 4.
14. If two nonvertical lines have slopes 3 and −1/3, what can be concluded?
A. They are parallel
B. They are identical
C. They are perpendicular
D. They have the same y-intercept
The product of perpendicular slopes is −1. Since 3(−1/3) = −1, the lines are perpendicular.
15. A quadratic function has zeros −2 and 5. Which factored form could represent the
function?
, A. (x − 2)(x + 5)
B. (x + 2)(x − 5)
C. (x − 2)(x − 5)
D. (x + 2)(x + 5)
Zeros at −2 and 5 correspond to factors x + 2 and x − 5.
16. What is the vertex of y = (x − 4)² + 7?
A. (−4, 7)
B. (4, −7)
C. (−4, −7)
D. (4, 7)
The vertex form y = (x − h)² + k has vertex (h, k), so the vertex is (4, 7).
17. Which statement about the graph of y = −x² + 6 is correct?
A. It opens upward
B. It opens downward
C. It is a line
D. It has no maximum
The negative leading coefficient causes the parabola to open downward, giving it a maximum
value.
18. What is the discriminant of x² − 6x + 9 = 0?
A. −36
B. 0
C. 9
D. 36
The discriminant is b² − 4ac = (−6)² − 4(1)(9) = 36 − 36 = 0.
19. What does a discriminant of zero indicate for a quadratic equation?
A. Two distinct real solutions
B. No real solutions
C. One repeated real solution
D. Two complex solutions
Answer: C
A zero discriminant means the quadratic has exactly one real solution counted twice.
2026/2027 | COMPLETE QUESTIONS AND ANSWERS
(VERIFIED ANSWERS) | EXAM PREP | LATEST EXAM
GUIDE 2026&2027
1. Which statement best describes the domain of the function f(x) = √(x − 4)?
A. x < 4
B. x ≤ 4
C. x ≥ 4
D. All real numbers
For a square-root function, the expression inside the radical must be nonnegative. Thus x − 4 ≥
0, giving x ≥ 4.
2. If f(x) = 3x − 7, what is f(5)?
A. 8
B. 15
C. 22
D. −8
Substituting x = 5 gives f(5) = 3(5) − 7 = 15 − 7 = 8.
3. Which equation represents a line with slope 4 and y-intercept −3?
A. y = −3x + 4
B. y = 4x − 3
C. y = 3x − 4
D. y = −4x − 3
Slope-intercept form is y = mx + b. With m = 4 and b = −3, the equation is y = 4x − 3.
4. A line passes through (2, 5) and (6, 13). What is its slope?
A. 1
B. 2
C. 3
D. 4
The slope is (13 − 5)/(6 − 2) = 8/4 = 2.
5. Which function is even?
,A. f(x) = x³ + x
B. f(x) = x² + 4
C. f(x) = x³ − 2
D. f(x) = x² + x
A function is even when f(−x) = f(x). For x² + 4, replacing x with −x produces the same
expression.
6. If f(x) = x² − 2x + 1, which form most clearly identifies the vertex?
A. (x − 1)²
B. (x + 1)²
C. x² − 2x
D. (x − 1)² + 1
Completing the square gives x² − 2x + 1 = (x − 1)², so the vertex is (1, 0).
7. What is the inverse of f(x) = 2x + 5?
A. f⁻¹(x) = 2x − 5
B. f⁻¹(x) = (x + 5)/2
C. f⁻¹(x) = (x − 5)/2
D. f⁻¹(x) = 5x − 2
Set y = 2x + 5, interchange x and y, and solve: x = 2y + 5, so y = (x − 5)/2.
8. If f(x) = x + 2 and g(x) = x², what is (g ∘ f)(3)?
A. 9
B. 11
C. 25
D. 15
First calculate f(3) = 5. Then apply g: g(5) = 25.
9. Which transformation changes f(x) into f(x − 6)?
A. Shift left 6 units
B. Shift right 6 units
C. Shift up 6 units
D. Shift down 6 units
Replacing x with x − 6 shifts the graph horizontally 6 units to the right.
10. What is the x-intercept of y = 2x − 10?
,A. −5
B. 2
C. 5
D. 10
At the x-intercept, y = 0. Therefore 0 = 2x − 10, giving x = 5.
11. Which expression is equivalent to (x² − 9)/(x − 3), where x ≠ 3?
A. x − 3
B. x + 3
C. x² + 3
D. x² − 6
Since x² − 9 = (x − 3)(x + 3), cancellation gives x + 3 for x ≠ 3.
12. What is the domain of f(x) = 1/(x + 7)?
A. x ≠ −7
B. x ≠ 7
C. x > −7
D. All real numbers
The denominator cannot equal zero. Therefore x + 7 ≠ 0, so x ≠ −7.
13. Which equation is equivalent to 2x + 3y = 12 in slope-intercept form?
A. y = 2x + 4
B. y = −2/3x + 4
C. y = 2/3x − 4
D. y = −3/2x + 12
Solving for y gives 3y = −2x + 12 and therefore y = −(2/3)x + 4.
14. If two nonvertical lines have slopes 3 and −1/3, what can be concluded?
A. They are parallel
B. They are identical
C. They are perpendicular
D. They have the same y-intercept
The product of perpendicular slopes is −1. Since 3(−1/3) = −1, the lines are perpendicular.
15. A quadratic function has zeros −2 and 5. Which factored form could represent the
function?
, A. (x − 2)(x + 5)
B. (x + 2)(x − 5)
C. (x − 2)(x − 5)
D. (x + 2)(x + 5)
Zeros at −2 and 5 correspond to factors x + 2 and x − 5.
16. What is the vertex of y = (x − 4)² + 7?
A. (−4, 7)
B. (4, −7)
C. (−4, −7)
D. (4, 7)
The vertex form y = (x − h)² + k has vertex (h, k), so the vertex is (4, 7).
17. Which statement about the graph of y = −x² + 6 is correct?
A. It opens upward
B. It opens downward
C. It is a line
D. It has no maximum
The negative leading coefficient causes the parabola to open downward, giving it a maximum
value.
18. What is the discriminant of x² − 6x + 9 = 0?
A. −36
B. 0
C. 9
D. 36
The discriminant is b² − 4ac = (−6)² − 4(1)(9) = 36 − 36 = 0.
19. What does a discriminant of zero indicate for a quadratic equation?
A. Two distinct real solutions
B. No real solutions
C. One repeated real solution
D. Two complex solutions
Answer: C
A zero discriminant means the quadratic has exactly one real solution counted twice.
