Directions: Please help with the following visual questions.

Note: THIS ISNT FOR AN ASSIGNMENT BUT MERELY FOR MY OWN UNDERSTANDING AND COMPREHENSION! PLEASE BE ORGINAL! THIS IS FOR PRACTICE.

Which of the following is the equation of the circle with center C and a point P on the circle, as shown in the graph? P 4 3 2 r = 10 -6 -5 -4 -3 -2 1 0 1 2 3 4 5 6 -1 -2 -3 C 4 -5 6 O (x - 4)2 + () + 5)2 = 10 O(x + 2)2 + (y-3)2 = 10 O(x - 2)2 + () + 3)2 = 100 O(x + 4)2 + (y - 5)2 = 100Given various values of the linear functions f (x) and g(x) in the table, determine the y-intercept of (f - g)(x). X -6 -4 -1 3 4 f (x) 15 11 5 -3 -5 g ( x) -36 -26 -11 9 14 O (0, 9) O (0, 3) O (0, -3) O (0, -9)If f (x) = 3x2 + 5x - 4, then "(*+)- is equal to which of the following? h (3x +3h)2 +(5x +5/)-4-(3x2 +5x -4) h 3(x +h)2+5x-4-3x2 -5x +4 h ( 3(x + h)2 +5(x+h)-4-3x2+5x-4 h ( 3 (x2 + 2xh+12)+5(x+1)-4-(3x2+5x-4) h Which of the following represents the difference quotient for f(x) =>? 3 O x(x +h) 3 O x(x +h) 3x +h x(h)(x+h) 3x +h x(h)(x+h) Determine 1(4 + h)-f(4) iff (x) = 3x - 2. h 03 O 2h O 3h(02.02 MC) Michael solved the system of linear equations and provided the solution. 3x - 3y = 6 4x - 7y = 2 4(3x -3y = 6) Step 1 -3(4x - 7y = 2) 12x - 12y = 24 Step 2 -12x + 21y = -6 Step 3 -33y = 30 Step 4 10 11 In which step did Michael show his first error? O Step 2 O Step 3 O Step 4 O No errors are present in the solution In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x2 + y2 = 5, and the path of the bean bag can be represented by y = 0.5x2 + 1.5x - 4. To which points could she have tossed her bean bag? O(-1, -2) or (-2, 1) O (1, -2) or (2, 1) O (-1, 2) or (-2, -1) O (1, 2) or (2, -1)Which of the following equations would correspond to a conic section formed when a plane intersects a cone at an angle parallel to the slant edge? Ox+ =32 22 Ox - By Which of the following conic sections could be formed when a plane intersects both cones of a double cone? O- 4 5 O- 78 5 4 3 2 -10Determine the domain and range of (g o f)(x) if f (X) = - 4 X- - 4 and g(x) = x + 2. OD: (X ER| x *-2, 2) and R: (-0o, 1) u (2, co) OD: (X E R| x *-4, 0} and R: (-0o, -2) u (2, 00) OD: (X E R| x *-4, -2, 0, 2} and R: (-0o, -1) u (2, co) OD: {X E R) and R: (-0o, -2) u (2, co) Given the following table with selected values of f (x) and g(x), evaluate f (9(4)). X -3 1 4 6 9 f (x) 2 4 9 1 -4 g(x) -6 1 4 6 9 3 O-4 O-2 02 09 Which of the following would not be a possible function for f (x) and g(x) such that (fog)(x) = 6 2+3? Of (x)= = +3 and g(x) = x Of (x) = 2 +3 and g(x) = x2 Of (x) = 2 +3 and 9(x) = =z Of (x)= =+ 3and g(x) =. * 2 3A right triangle is shown in the graph. y (a, y) b (a, b) Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (a, b) and a point on the circle at (x, y). Show all necessary math work. Part B: If (a, b) = (5, -2) and c = 10, determine the domain and range of the circle. Part C: Is the point (10, 2) inside the border of the circle if (a, b) = (5, -2) and c = 10? Explain using mathematical evidence.Which graph represents two functions that are increasing on all points across the domain that is common to both functions? h() i(2) h(x) j(=) h(x) i(z) O 4 -3 3 -1 i(2) What is the interval in which both / (x) and g(x) are negative? 9(2) -10 -9 - S(=) O (-oo, 2) u (2, 09) (2, 09) O (3, 09) O (6, 09)\fGiven the following table with selected values of the functions / (x) and gu), determine / (9(2)) - g//(-1). 4 -1 2 4 7 f (x) 17 -1 -7 -9 -27 -10 -8 -2 4 8 14 O-7 O-5 O-2 01 A railroad's track can be determined using the following graph. -10 -0 8 -7 -8 -5 -4 -3 -2 -19 12 3 4 5 8 7 10 Several different roadways are in the same region as the railroad. Part A: A highway's path can be found using the equation 2x + 3y = 21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely Part B: A turnpike's route is determined by the equation y= =x". Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary work. An ice cube is freezing in such a way that the side length s, in inches. is s() - -1+6, where & is in hours. The surface area of the ice cube is the function A(s) = Gs?. Part A: Write an equation that gives the volume at t hours after freezing begins. Part B: Find the surface area as a function of time, using composition, and determine its range. Part C: After how many hours will the surface area equal 384 square inches? Show all necessary calculationsf(x) 9(x) 10 -NWAMO NOD -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 3 4 5 6 7 8 9 10 20 The graphs of f(x) = --x3 and g(x) = -log2(x + 3) have which of the following features in common? Ox-Intercept O Range O End behavior O Vertical asymptote Given f (x) = x2 + 6x + 8 and g(x) = x3 + 2x2 - 9x - 18, find the domain of O(x E R} Ofx E R| x * -2, -3, 3} O (x E R| x * -3, 3} O(x E Rx # -4) How many solutions does the system of equations x - y = -4 and y = v2x +3 -2 have? O Infinitely many Oo 1 2Which conic section is formed in the image shown? O Circle O Parabola O Ellipse O Hyperbola To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone? O The plane is parallel to the base of the cone. O The plane may be perpendicular to the base of the cone. O The plane is at an angle that is neither parallel nor perpendicular to the base of the cone. O The plane must be at a 45 angle to the base of the cone.owing graphs s s() s(t) The graphs of f () -13 + x - 6x - 1 and god - e" - 2 have which of the following features in common? O Range Ox-intercept Oy-intercept OEnd behavior What values does the function / (x) = \\x + 1- 3 have in its range that are not in the range of the graph of glx)? Of-3.-1) OF-3-1)A pool is built in the shape of an ellipse, centered at the origin. The maximum vertical length is 30 feet, and the maximum horizontal width is 14 feet. Which of the following equations represents the pool? O + 1 225 49 O = 1 225 49 O + = 1 900 196 O + =1 900 196Based on the graphs of f (x) and g(x), what must the domain of (f . g)(x) ba? to w -10 9 -0 -7 -6 -5 -4 -3 -2 -1 2 3 675 8 f(@) Of E R) Of* =R|x *-2, 3) Ofx = R | x .