WebAssign hw1.1 (Homework) Current Score : / 71 Due : Wednesday, May 31 2017 07:25 AM PDT Michael Lee Math261(Calculus I), section 1049, Spring 2017 Instructor: Michael Lee 1. /1 pointsscalc8 1.1.002. If f(x) = x 2 9x x 9 and g(x) = x is it true that f = g? Yes No 2. /3 pointsscalc8 1.1.007. 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 http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 1/21
3. /3 pointsscalc8 1.1.008. 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 http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 2/21
4. /3 pointsscalc8 1.1.009. 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 http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 3/21
5. /2 pointsscalc8 1.1.014. 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 http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 4/21
6. /1 pointsscalc8 1.1.018. 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. http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 5/21
7. /10 pointsscalc8 1.1.025. 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 pointsscalc8 1.1.028.MI. Evaluate the difference quotient for the given function. Simplify your answer. f(x) = x 3, f(a + h) f(a) h http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 6/21
9. /1 pointsscalc8 1.1.029. Evaluate the difference quotient for the given function. Simplify your answer. 1 f(x) =, x f(x) f(a) x a 10. /1 pointsscalc8 1.1.031. Find the domain of the function. (Enter your answer using interval notation.) f(x) = x + 4 x 2 49 11. /1 pointsscalc8 1.1.033. Find the domain of the function. (Enter your answer using interval notation.) 3 f(t) = 5t 8 12. /1 pointsscalc8 1.1.035. Find the domain of the function. (Enter your answer in interval notation.) h(x) = 4 1 x 2 3x http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 7/21
13. /3 pointsscalc8 1.1.038. 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. http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 8/21
14. /4 pointsscalc8 1.1.041. 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. http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 9/21
15. /1 pointsscalc8 1.1.049. Sketch the graph of the function. f(x) = 3 x if x 1 3 if x > 1 http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 10/21
16. /2 pointsscalc8 1.1.051. 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 pointsscalc8 1.1.053. Find an expression for the function whose graph is the given curve. y = The bottom half of the parabola x + (y 7) 2 = 0 18. /1 pointsscalc8 1.1.054. 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 http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 11/21
19. /2 pointsscalc8 1.1.057. 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 pointsscalc8 1.1.058. 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.) http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 12/21
21. /2 pointsscalc8 1.1.059. 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 pointsscalc8 1.1.061. 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.) http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 13/21
23. /1 pointsscalc8 1.1.062. 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 pointsscalc8 1.1.063. 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) = http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 14/21
25. /4 pointsscalc8 1.1.069. 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. http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 15/21
26. /4 pointsscalc8 1.1.070. 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. http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 16/21
27. /2 pointsscalc8 1.1.071. (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 pointsscalc8 1.1.073. 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 2 + 1 odd neither 29. /1 pointsscalc8 1.1.074. 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 4 + 3 even odd neither http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 17/21
30. /1 pointsscalc8 1.1.075. 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 31. /1 pointsscalc8 1.1.508.XP. Find the domain of the function. (Enter your answer using interval notation.) g(x) = x x 2 http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 18/21
32. /2 pointsscalc8 1.1.515.XP. Find the domain of the function. (Enter your answer using interval notation.) G(x) = 5x + x x Sketch the graph of the function. http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 19/21
33. /2 pointsscalc8 1.1.520.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, ) http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 20/21
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, ) http://www.webassign.net/web/student/assignment Responses/last?dep=15776521 21/21