Review Chapter 1 (Q10,12)

5. Use the graph of the function fshown to the right to answer parts (a)-(n). (a) Find r( - 21) and ts). f= E i6): E (b) Find 1 a) and 0). m): |:| fw>= |:| (C) Is f(6) positive or negative? 0 Positive 0 Negative (d) Is f( - 6) positive or negative? 0 Positive 0 Negative (e) For what value(s) of x is f(x) = 0? (Use a comma to separate answers as needed.) (f) For what values of x is f(x) > 0? |:| (Type a compound inequality. Use a comma to separate answers as needed.) (9) What is the domain of f? The domain off is {x| :1}. (Type a compound inequality.) (h) What is the range off? The range off is {y| :|}. (Type a compound inequality.) (i) What are the x-intercept(s)? (Type an integer or a simplied fraction. Use a comma to separate answers as needed.) (j) What are the y-intercept(s)? (Type an integer or a simplied fraction. Use a comma to separate answers as needed.) (k) How often does the line y = 1 intersect the graph? time(s) (1) How often does the line x = 5 intersect the graph? time(s) (m) For what value(s) of x does f(x) = -6? X= (Use a comma to separate answers as needed.) (n) For what value(s) of x does f(x) = 9? X = (Use a comma to separate answers as needed.)6. Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to nd (a) its domain and range. (b) the intercepts, if any. (c) any symmetry with respect to the x-axis, y-axis, or the origin. Is the graph that of a function? 0 Yes If the graph is that of a function, what are the domain and range of the function? Select the correct choice below and, if necessary, ll in the answer box to complete your choice. 0 A- The domain is |:| The range is |:|. (Type your answers in interval notation.) O B. The graph is not that of a function. If the graph is that of a function, what are the intercepts of the function? Select the correct choice below and. if necessary. ll in the answer box to complete your choice. 0 A- The intercept(s) isl'are |:|. (Type an ordered pair. Use a comma to separate answers as needed.) 0 B. The graph is not that of a function. If the graph is that of a function, determine what kinds of symmetry it has. Select all that apply. E] A. The graph is a function and is symmetrical with respect to the origin. E] B. The graph is a function and is symmetrical with respect to the y-axis. E] C. The graph is a function and is symmetrical with respect to the x-axis. E] D. The graph is a function and is not symmetrical. E] E. The graph is not that of a function. 7. Determine whether the graph on the right is that of a function by using the vertical-line test. If it y Q is, use the graph to nd the following. ' (a) the domain and range (assume that the curve approaches but never intersects the y-axis) (b) the intercepts, if any (c) any symmetry with respect to the x-axis, y-axis, or the origin Does the graph represent a function? Choose the correct answer below. 0 A. No, the graph is not a function because a vertical line x = 4 intersects the graph at only one point. 0 B. Yes, the graph is a function because every vertical line intersects the graph in at most one point. 0 C. Yes, the graph is a function because every vertical line intersects the graph in more than one point. 0 D. No, the graph is not a function because a vertical line x = 4 intersects the graph at two points. (a) What are the domain and range of the function? Select the correct choice below and, if necessary, ll in the answer box(es) to complete your choice. 0 A- The domain is |:|. The range is |:|. (Type your answers in interval notation. Use integers or fractions for any numbers in the expressions.) 0 B. The graph is not that of a function. (b) What isiare the intercept(s)? Select the correct choice below and. if necessary. ll in the answer box to complete your choice. 0 A- The intercept(s) islare |:|. (Type an ordered pair. Use a comma to separate answers as needed.) 0 B. There are no intercepts. O C. The raph is not that of a function. 9 (c) Determine if the graph is symmetric with respect to the x-axis. y-axis, or the origin. Select all that apply. E] A. The graph is symmetric with respect to the y-axis. E] B. The graph is symmetric with respect to the xaxis. C] C. The graph is symmetric with respect to the origin. E] D. The graph has no symmetry. E] E. The graph is not that of a function. 8. Answer the questions about the following function. (a) Choose the correct answer below. f (x) = - x + 12 O A. x - 2 19 No, because substituting x = 6 into the given equation does not result in -. (a) Is the point |6, on the graph of f? O B. No, because substituting x = - into the given equation does not result in 6. (b) If x = 3, what is f(x)? What point is on the graph of f? (c) If f(x) = 2, what is x? What point(s) is (are) on the graph of f? O C. (d) What is the domain of f? Yes, because substituting x = 6 into the given equation results in (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. OD. 19 Yes, because substituting x = - into the given equation results in 6. (b) If x = 3, f(x) = (Simplify your answer.) Using the information in the previous step, list the point(s) on the graph of f, where x = 3. (Simplify your answer. Type an ordered pair.) (c) If f(x) = 2, x = Simplify your answer. Use a comma to separate answers as needed.) Using the information in the previous step, list the point(s) on the graph of f, where f(x) = 2 (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) (d) What is the domain of f? The domain is (Type your answer in interval notation.) (e) List the x-intercept(s), if any, of the graph of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The x-intercept(s) is/are Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O B. There are no x-intercepts. (f) List the y-intercept, if any, of the graph of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The y-intercept(s) is/are Type an integer or a simplified fraction. Use a comma to separate answers as needed) O B. There is no y-intercept.9. Match the following functions with the graph. (3) The cost of painting a wall as a function of its square footage. (b) The height of an egg dropped from a 300foot building as a function of time. (c) The height of an animal as a function of time. (d) The demand for energy drink as a function of price. (a) The height of a pendulum bob as a function of time. (a) (b) (c) (d) (1) (2) (3) (4) (5) (HONOI {2)0Iv 0| (310v on OIII OIII OIII 0V OII ON ON 0v 0| ,0 In" p9 IV ,op In" 10. Write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). Then graph the circle. r= 10; (h,k)=(8, -6) The standard form of the equation of this circle is (was)2 +(y+6)2 = 100. The general form of the equation of this circle is :l. (Simplify your answer.) Graph the circle. .p. ,0 '9" 12. For the equation x + y - 2x - 4y - 4 =0, do the following. + (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any. (a) The center is (1,2) (Type an ordered pair.) 2- The radius is r = X 3 10 -8 6 4 8 16 (b) Use the graphing tool to graph the circle. (c) Find the intercepts, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed. Type exact answers for each coordinate, using radicals as needed.) O B. There is no intercept.1. 1 If x = - 4, nd the value of the expression 3x2 6x + ;. 1 287 If x = - 4, the value of the expression 3x2 - 6x + ; is T . (Type an integer or a decimal.) 8' Find the following for the function f(x) = 4x2 + 4x 2. (a) f(0) (b) 1'0) (c) f( ' 1) (d) f( - X) (e) f(x) (mews) (g)f(3x) (h)f(x+h) (a) f(0) = - 2 (Simplify your answer.) (b) f(1) = 6 (Simplify your answer.) (6) f( 1) = 2 (Simplify your answer.) (d) f( - x) = 4x2 - 4x - 2 (Simplify your answer.) (a) - f(x) = - 4x2 - 4x + 2 (Simplify your answer.) (f) f(x + 3) = 4x2 + 28x + 46 (Simplify your answer.) (9) f(3x) = 36x2 + 12x - 2 (Simplify your answer.) (h) f()( + h) = 4x2 + x(8h + 4) + 4h2 + 4h 2 (Simplify your answer.) 10. Find the domain of the function. The domain is . (Type your answer in interval notation.) 11. Find the domain of the function. Vt - 6 P(t) = 2t - 14 The domain is X> 7 (Type your answer in interval notation.)1. Complete the sentence the below. If the point (4, - 1) is a point on the graph of f, then f( _ ) = . If the point (4, 1) is a point on the graph of f, then f(|:|) = |:|. 2- Find a so that the point (- 1,2) is on the graph of f(x) = ax2 + 5. a = |:| (Simplify your answer.) 3. Determine whether the statement below is true or false. The graph of a function y = f(x) always crosses the yaxis. Choose the correct answer below. 0 False 0 True 4. Decide whether the following statement is true or false. The y-intercept of the graph of the function y = f(x), whose domain is all real numbers, is f(0). Choose the correct answer below