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Concept explainers
a.
To find the value of
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 12RE
The answer is
Explanation of Solution
Given:
The graph of function f is given.
Concept Used:
The concept of graphing of functions is used.
In the graph, when x = -2 , y = -1. So
b.
To find the domain of f .
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 12RE
The domain of
Explanation of Solution
Given:
The graph of function f is given.
Concept Used:
The concept of domain of functions is used.
In the graph, x can take values between -4 and 5, both included. Hence the domain of f = [-4, 5].
c.
To find the range of f .
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 12RE
The range of
Explanation of Solution
Given:
The graph of function f is given.
Concept Used:
The concept of range of functions is used.
In the graph, y can take values between -4 and 4, both included. Hence the range of f = [-4, 4].
d.
To tell the intervals where f is increasing and decreasing.
d.
![Check Mark](/static/check-mark.png)
Answer to Problem 12RE
The intervals where f is increasing are: (-4, -2) and (0, 4).
The intervals where f is decreasing are: (-2, 0) and (4, 5).
Explanation of Solution
Given:
The graph of function f is given.
Concept Used:
The concept of increasing and decreasing functions is used.
The intervals where f is increasing are: (-4, -2) and (0, 4).
The intervals where f is decreasing are: (-2, 0) and (4, 5).
e.
To find the
e.
![Check Mark](/static/check-mark.png)
Answer to Problem 12RE
The local maximum value of f = 4 at x=4.
Explanation of Solution
Given:
The graph of function f is given.
Concept Used:
The concept of local maximum value of functions is used.
The local maximum value of f =4 at x=4.
e.
To check if
e.
![Check Mark](/static/check-mark.png)
Answer to Problem 12RE
No, f is not one to one.
Explanation of Solution
Given:
The graph of function f is given.
Concept Used:
The concept of one to one functions is used.
In the graph of f, f(-2)=f(0). Hence the function f is not one to one.
Chapter 2 Solutions
EBK PRECALCULUS: MATHEMATICS FOR CALCUL
- Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below. Let g(x) = √ƒƒ(t) dt . 0 3 2 -2 2 4 5 6 7 8 9 10 11 12 13 14 15 1. g(0) = 2. g(2) = 3. g(4) = 4. g(6) = 5. g'(3) = 6. g'(13)=arrow_forwardThe expression 3 | (3+1/+1) of the following integrals? A Ов E + + + + 18 3+1+1 3++1 3++1 (A) √2×14 dx x+1 (C) 1½-½√ √ ² ( 14 ) d x (B) √31dx (D) So 3+x -dx is a Riemann sum approximation of which 5 (E) 1½√√3dx 2x+1arrow_forward2. Suppose the population of Wakanda t years after 2000 is given by the equation f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000 people? Show all your work, round your answer to two decimal places, and include units. (4 points)arrow_forward
- 3. Solve the equation, give the answer exactly (no calculator approximations), and show all your work. (4 points) log5 2x = 3arrow_forwardLet I = f(x) dx, where f is the function whose graph is shown. 4 2 y f X 1 2 3 4 (a) Use the graph to find L2, R2 and M2. R₂ M2 = = = (b) Are these underestimates or overestimates of I? O 42 is an underestimate. O 42 is an overestimate. ◇ R2 is an underestimate. OR2 is an overestimate. OM2 is an underestimate. ○ M2 is an overestimate. (c) Use the graph to find T2. T₂ =arrow_forwardVector u has a magnitude of 23 and vector v has a magnitude of 83. The angle between the two vectors is 126 degrees.a) Draw a fully-labelled vector diagram showing the two vectors and the resultant vector when they are added together.b) Find the magnitude of the resultant vector.c) Find the direction of the resultant vector relative to vector u. Solding by finding the x and y of the vectors and addingarrow_forward
- 3) If a is a positive number, what is the value of the following double integral? 2a Love Lv 2ay-y² .x2 + y2 dadyarrow_forward16. Solve each of the following equations for x. (a) 42x+1 = 64 (b) 27-3815 (c) 92. 27² = 3-1 (d) log x + log(x - 21) = 2 (e) 3 = 14 (f) 2x+1 = 51-2xarrow_forward11. Find the composition fog and gof for the following functions. 2 (a) f(x) = 2x+5, g(x) = x² 2 (b) f(x) = x²+x, g(x) = √√x 1 (c) f(x) = -1/2) 9 9(x) = х = - Xarrow_forward
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