WebAssign hw1.1 (Homework)

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1 WebAssign hw1.1 (Homework) Current Score : / 71 Due : Wednesday, May :25 AM PDT Michael Lee Math261(Calculus I), section 1049, Spring 2017 Instructor: Michael Lee 1. /1 pointsscalc If f(x) = x 2 9x x 9 and g(x) = x is it true that f = g? Yes No 2. /3 pointsscalc Consider the following graph. Determine whether the curve is the graph of a function of x. Yes, it is a function. No, it is not a function. If it is, state the domain and range of the function. (Enter your answers in interval notation. If the curve is not the graph of a function of x, enter DNE.) domain range Responses/last?dep= /21

2 3. /3 pointsscalc Consider the following graph. Determine whether the curve is the graph of a function of x. Yes, it is a function. No, it is not a function. If it is, state the domain and range of the function. (Enter your answers using interval notation. If it is not a function, enter DNE in all blanks.) domain range Responses/last?dep= /21

3 4. /3 pointsscalc Consider the following graph. Determine whether the curve is the graph of a function of x. Yes, it is a function. No, it is not a function. If it is, state the domain and range of the function. (Enter your answers using interval notation. If it is not a function, enter DNE in all blanks.) domain range Responses/last?dep= /21

4 5. /2 pointsscalc Three runners compete in a 100 meter race. The graph depicts the distance run as a function of time for each runner. Describe in words what the graph tells you about this race. Who won the race? runner A runner B runner C Did each runner finish the race? Yes No Responses/last?dep= /21

5 6. /1 pointsscalc Sketch a rough graph of the market value of a new car as a function of time for a period of 20 years. Assume the car is well maintained. Responses/last?dep= /21

6 7. /10 pointsscalc If f(x) = 4x 2 x + 3, f(2) = f( 2) = find the following. f(a) = f( a) = f(a + 1) = 2f(a) = f(2a) = f(a 2 ) = [f(a)] 2 = f(a + h) = 8. /1 pointsscalc MI. Evaluate the difference quotient for the given function. Simplify your answer. f(x) = x 3, f(a + h) f(a) h Responses/last?dep= /21

7 9. /1 pointsscalc Evaluate the difference quotient for the given function. Simplify your answer. 1 f(x) =, x f(x) f(a) x a 10. /1 pointsscalc Find the domain of the function. (Enter your answer using interval notation.) f(x) = x + 4 x /1 pointsscalc Find the domain of the function. (Enter your answer using interval notation.) 3 f(t) = 5t /1 pointsscalc Find the domain of the function. (Enter your answer in interval notation.) h(x) = 4 1 x 2 3x Responses/last?dep= /21

8 13. /3 pointsscalc Find the domain and range of the function. (Enter your answers using interval notation.) h(x) = 81 x 2 domain range Sketch the graph of the function. Responses/last?dep= /21

9 14. /4 pointsscalc Evaluate f( 5), f(0), and f(4) for the piecewise defined function. f(x) = f( 5) = f(0) = f(4) = x + 2 if x < 0 1 x if x 0 Sketch the graph of the function. Responses/last?dep= /21

10 15. /1 pointsscalc Sketch the graph of the function. f(x) = 3 x if x 1 3 if x > 1 Responses/last?dep= /21

11 16. /2 pointsscalc Find an expression for the function whose graph is the given curve. (Assume that the points are in the form (x, f(x)).) f(x) = The line segment joining the points (1, 3), and (5, 3) Find the domain of the function. (Enter your answer using interval notation.) 17. /1 pointsscalc Find an expression for the function whose graph is the given curve. y = The bottom half of the parabola x + (y 7) 2 = /1 pointsscalc Find an expression for the function whose graph is the given curve. y = The top half of the circle x 2 + (y 1) 2 = 1 Responses/last?dep= /21

12 19. /2 pointsscalc Find a formula for the described function. A rectangle has perimeter 16 m. Express the area A of the rectangle as a function of the length, L, of one of its sides. A = m 2 State the domain of A. (Assume the length of the rectangle is longer than its width. Enter your answer in interval notation.) 20. /2 pointsscalc Find a formula for the described function. A rectangle has area 81 m 2. Express the perimeter of the rectangle as a function of the length L of one of its sides. P(L) = State the domain of P. (Assume the length of the rectangle is larger than its width. Enter your answer using interval notation.) Responses/last?dep= /21

13 21. /2 pointsscalc Find a formula for the described function. Express the area of an equilateral triangle as a function of the length of a side x. A(x) = State the domain of A. (Enter your answer using interval notation.) 22. /2 pointsscalc Find a formula for the described function. An open rectangular box with volume 6 m 3 has a square base. Express the surface area SA of the box as a function of the length of a side of the base, x. SA = m 2 State the domain of SA. (Enter your answer in interval notation.) Responses/last?dep= /21

23. /1 pointsscalc8 1.1.062. A Norman window has the shape of a rectangle surmounted by a semicircle.

of the window. A(x) = 24. /1 pointsscalc8 1.1.063.

14 23. /1 pointsscalc A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 18 ft, express the area A of the window as a function of the width x of the window. A(x) = 24. /1 pointsscalc A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. V(x) = Responses/last?dep= /21

15 25. /4 pointsscalc Graphs of f and g are shown. Is f even, odd, or neither? even odd neither Explain your reasoning. It is symmetric about the origin. It is symmetric with respect to the y axis. It is symmetric with respect to the x axis. It is not symmetric about the origin or the y axis. Is g even, odd, or neither? even odd neither Explain your reasoning. It is symmetric about the origin. It is symmetric with respect to the y axis. It is symmetric with respect to the x axis. It is not symmetric about the origin or the y axis. Responses/last?dep= /21

16 26. /4 pointsscalc Graphs of f and g are shown. Is f even, odd, or neither? even odd neither Explain your reasoning. It is symmetric about the origin. It is symmetric with respect to the y axis. It is symmetric with respect to the x axis. It is not symmetric about the origin or the y axis. Is g even, odd, or neither? even odd neither Explain your reasoning. It is symmetric about the origin. It is symmetric with respect to the y axis. It is symmetric with respect to the x axis. It is not symmetric about the origin or the y axis. Responses/last?dep= /21

17 27. /2 pointsscalc (a) If the point (3, 9) is on the graph of an even function, what other point must also be on the graph? (x, y) = (b) If the point (3, 9) is on the graph of an odd function, what other point must also be on the graph? (x, y) = 28. /1 pointsscalc Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. f(x) = even x x odd neither 29. /1 pointsscalc Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. x f(x) = 2 x even odd neither Responses/last?dep= /21

18 30. /1 pointsscalc Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. even odd f(x) = neither x x /1 pointsscalc XP. Find the domain of the function. (Enter your answer using interval notation.) g(x) = x x 2 Responses/last?dep= /21

19 32. /2 pointsscalc XP. Find the domain of the function. (Enter your answer using interval notation.) G(x) = 5x + x x Sketch the graph of the function. Responses/last?dep= /21

20 33. /2 pointsscalc XP. Find a formula for the described function. Express the surface area of a cube as a function of its volume V. SA(V) = State the domain of SA(V). (Enter your answer using interval notation.) 34. /1 pointsscalc8 1.1.JIT.008.MI. Find the domain of the function. G(x) = x 2 64 (8, ) [8, ) (, 8) (8, ) (, 8] (, ) (, 8] [8, ) 35. /1 pointsscalc8 1.1.JIT.009.MI. Find the domain of the function. g(x) = (, ) x 8x 2 + 7x 1 [0, 1/8) (1/8, ) (, 1) (8, ) (, 1/8) (1/8, ) [0, 8) (8, ) Responses/last?dep= /21

21 36. /1 pointsscalc8 1.1.JIT.010.MI. Find the domain of the function. f(x) = 4 x 1 x 2 ( 1, 1) (, ) (, 1) (1, ) (, 1] (, 1) (1, ) Responses/last?dep= /21

WebAssign hw2.2 (Homework)

WebAssign hw2.2 (Homework) Current Score : / 92 Due : Wednesday, May 31 2017 07:25 AM PDT Michael Lee Math261(Calculus I), section 1049, Spring 2017 Instructor: Michael Lee 1. /2 pointsscalc8 1.5.001.