Test Bank For Precalculus
Chapter 1 Form A: Test
1. Use interval notation to list the values of x that satisfy the inequality x2 − 3x + 2 ≤ 0.
2. Find all values of x that solve the equation |6x − 3| = 9.
3. Solve the inequality |x − 3| ≥ 2 and write the solution using interval notation.
4. Consider the points P1(2, 4) and P2(−1, 3)
(a) Find the distance between P1 and P2.
(b) Find the midpoint of the line segment joining P1 and P2.
5. Indicate on the xy-plane the points (x, y) for which the statement
|x − 1| < 3 and |y + 1| < 2
holds.
6. Find the equation of the circle shown in the figure.
y
5
x
7. Consider the circle with equation x2 + 2x + y2 − 4y = −4.
(a) Find the center of the circle.
(b) Find the radius of the circle.
8. Specify any axis or origin symmetry of the graph.
y
x
9. Consider the equation y = x3 + 8.
(a) Determine any axis intercepts of the equation.
(b) Describe any axis or origin symmetry of the equation.
10. Find the distance between the points of intersection of the graphs y = x2 + 2 and y = 6.
1
, Test Bank For Precalculus
11. Suppose f (x) = 4x2 + 1. Find the following values.
√
(a) f (2) (c) f (2 + 3) (e) f (2x) (g) f (x + h)
√ √
(b) f ( 3) (d) f (2) + f ( 3) (f) f (1 − x) (h) f (x + h) − f (x)
12. The graph of the function f is given in the figure.
y
5
4
3
2
1 2 3 4 5 x
(a) Determine the value of f (−2). (d) Determine the value of f (3).
(b) Determine the value of f (0). (e) Determine the domain of the function f .
(c) Determine the value of f (2). (f) Determine the range of the function f .
13. Consider the following graph.
y
1.5
1
1 2 x
(a) Use the graph to determine the domain of the function.
(b) Use the graph to determine the range of the function.
14. Find the domain of each function.
√
(a) f (x) = 3x +1 (c) f (x) =
3x +1
1 1
(b) f (x) = (d) f (x) = √
3x +1 3x +1
2
, Test Bank For Precalculus
15. Suppose that f (x) = 2x − 4.
(a) Find f (x + h). (b) Find f (x + h) − f (x).
(c) Find f(x+h)−f(x)
h
when h /= 0.
(d) Find the value that f(x+h)−f(x)
h
approaches as h → 0.
16. Express the area A of an equilateral triangle as a function of x if the side length is 3x.
17. Find the equation of the line that passes through the point (2, 3) and has slope −2.
18. Find the slope-intercept form of the equation of the line that passes (0, 0) through and is parallel to
y = 2x + 1.
19. Find the slope-intercept equation of the line that has x-intercept −2 and y-intercept −3.
20. A new computer workstation costs $10,000. Its useful lifetime is 4 years, at which time it will be worth
an estimated $2000. The company calculates its depreciation using the linear decline method that is
an option in the tax laws. Find the linear equation that expresses the value V of the equipment as a
function of time t, for 0 ≤ t ≤ 4.
21. Consider the parabola with equation y = x2 − 4x + 3.
(a) Determine the vertex of the parabola.
(b) Sketch the graph of the parabola.
22. Suppose that f (x) = −x2 + 6x − 8.
(a) Express the quadratic in standard form. (c) Find the maximum value of the function.
(b) Find any axis intercepts. (d) Find the minimum value of the function.
√
23. Find the domain of the function described by f (x) = x2 − 3.
24. A rectangle is inscribed beneath the parabola with equation y = 4
— x2. Express the area of the
rectangle as a function of x.
y
5
x 5 x
25. Consider the parabola with equation y = (x − 3)2.
(a) Determine the vertex of the parabola.
(b) Sketch the graph of the parabola.
3
, Test Bank For Precalculus
Chapter 1 Form A: Answers
1. [1, 2]
2. x = −1,x = 2
3. (−∞, 1] ∪ [5, ∞)
√ 1 7
4. d = 10, midpoint= ,
2 2
5.
y
5
5 x
6. (x + 2)2 + (y − 3)2 = 16
7. center: (−1, 2); radius: 1
8. origin
9. (a) (−1, 0) and (0, 1)
(b) none
10. 4
11. (a) 17 (d) 30 (g) 4x2 + 8xh + 4h2 +1
(b) 13 (e) 16x2 +1 (h) 8xh + 4h2
√
(c) 29+ 16 3 (f) 5 − 8x + 4x2
12. (a) −2.5 (c) 2 (e) [−3.5, 3]
(b) −0.5 (d) 0 (f) [−4, 0) ∪ (0, 2.25]
13. domain: (−∞, ∞); range: (1, ∞) ∪ {−1}
14. (a) (−∞, ∞) 1
(c) − ,∞
3
1 1 1
(b) −∞, − ∪ − ,∞ (d) − , ∞
3 3 3
15. (a) 2x + 2h − 4 (b) 2h (c) 2 (d) 2
√
9 3
16. A = x
4
17. y = −x +5
18. y = 2x
3
19. y = − x − 3
2
4
Chapter 1 Form A: Test
1. Use interval notation to list the values of x that satisfy the inequality x2 − 3x + 2 ≤ 0.
2. Find all values of x that solve the equation |6x − 3| = 9.
3. Solve the inequality |x − 3| ≥ 2 and write the solution using interval notation.
4. Consider the points P1(2, 4) and P2(−1, 3)
(a) Find the distance between P1 and P2.
(b) Find the midpoint of the line segment joining P1 and P2.
5. Indicate on the xy-plane the points (x, y) for which the statement
|x − 1| < 3 and |y + 1| < 2
holds.
6. Find the equation of the circle shown in the figure.
y
5
x
7. Consider the circle with equation x2 + 2x + y2 − 4y = −4.
(a) Find the center of the circle.
(b) Find the radius of the circle.
8. Specify any axis or origin symmetry of the graph.
y
x
9. Consider the equation y = x3 + 8.
(a) Determine any axis intercepts of the equation.
(b) Describe any axis or origin symmetry of the equation.
10. Find the distance between the points of intersection of the graphs y = x2 + 2 and y = 6.
1
, Test Bank For Precalculus
11. Suppose f (x) = 4x2 + 1. Find the following values.
√
(a) f (2) (c) f (2 + 3) (e) f (2x) (g) f (x + h)
√ √
(b) f ( 3) (d) f (2) + f ( 3) (f) f (1 − x) (h) f (x + h) − f (x)
12. The graph of the function f is given in the figure.
y
5
4
3
2
1 2 3 4 5 x
(a) Determine the value of f (−2). (d) Determine the value of f (3).
(b) Determine the value of f (0). (e) Determine the domain of the function f .
(c) Determine the value of f (2). (f) Determine the range of the function f .
13. Consider the following graph.
y
1.5
1
1 2 x
(a) Use the graph to determine the domain of the function.
(b) Use the graph to determine the range of the function.
14. Find the domain of each function.
√
(a) f (x) = 3x +1 (c) f (x) =
3x +1
1 1
(b) f (x) = (d) f (x) = √
3x +1 3x +1
2
, Test Bank For Precalculus
15. Suppose that f (x) = 2x − 4.
(a) Find f (x + h). (b) Find f (x + h) − f (x).
(c) Find f(x+h)−f(x)
h
when h /= 0.
(d) Find the value that f(x+h)−f(x)
h
approaches as h → 0.
16. Express the area A of an equilateral triangle as a function of x if the side length is 3x.
17. Find the equation of the line that passes through the point (2, 3) and has slope −2.
18. Find the slope-intercept form of the equation of the line that passes (0, 0) through and is parallel to
y = 2x + 1.
19. Find the slope-intercept equation of the line that has x-intercept −2 and y-intercept −3.
20. A new computer workstation costs $10,000. Its useful lifetime is 4 years, at which time it will be worth
an estimated $2000. The company calculates its depreciation using the linear decline method that is
an option in the tax laws. Find the linear equation that expresses the value V of the equipment as a
function of time t, for 0 ≤ t ≤ 4.
21. Consider the parabola with equation y = x2 − 4x + 3.
(a) Determine the vertex of the parabola.
(b) Sketch the graph of the parabola.
22. Suppose that f (x) = −x2 + 6x − 8.
(a) Express the quadratic in standard form. (c) Find the maximum value of the function.
(b) Find any axis intercepts. (d) Find the minimum value of the function.
√
23. Find the domain of the function described by f (x) = x2 − 3.
24. A rectangle is inscribed beneath the parabola with equation y = 4
— x2. Express the area of the
rectangle as a function of x.
y
5
x 5 x
25. Consider the parabola with equation y = (x − 3)2.
(a) Determine the vertex of the parabola.
(b) Sketch the graph of the parabola.
3
, Test Bank For Precalculus
Chapter 1 Form A: Answers
1. [1, 2]
2. x = −1,x = 2
3. (−∞, 1] ∪ [5, ∞)
√ 1 7
4. d = 10, midpoint= ,
2 2
5.
y
5
5 x
6. (x + 2)2 + (y − 3)2 = 16
7. center: (−1, 2); radius: 1
8. origin
9. (a) (−1, 0) and (0, 1)
(b) none
10. 4
11. (a) 17 (d) 30 (g) 4x2 + 8xh + 4h2 +1
(b) 13 (e) 16x2 +1 (h) 8xh + 4h2
√
(c) 29+ 16 3 (f) 5 − 8x + 4x2
12. (a) −2.5 (c) 2 (e) [−3.5, 3]
(b) −0.5 (d) 0 (f) [−4, 0) ∪ (0, 2.25]
13. domain: (−∞, ∞); range: (1, ∞) ∪ {−1}
14. (a) (−∞, ∞) 1
(c) − ,∞
3
1 1 1
(b) −∞, − ∪ − ,∞ (d) − , ∞
3 3 3
15. (a) 2x + 2h − 4 (b) 2h (c) 2 (d) 2
√
9 3
16. A = x
4
17. y = −x +5
18. y = 2x
3
19. y = − x − 3
2
4
