Exam (elaborations)
Test Bank For Precalculus - 5th - 2012 All Chapters - 9780840068620
- Course
- Institution
Test Bank For Precalculus - 5th - 2012 All Chapters
[Show more]
Content preview
Test Bank For PrecalculusChapter 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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller TestBankNursingUS. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $49.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
79271 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now