Compositions of Functions Maze! Hunter Bimey Directions: Use the given functions to solve the problems below. Use your solutions to navigate through the maze. Staple all work to this paper! g(x) = = 3x + 1 h(x) = 5 x j(x) = x² + 7 k(x) = x² + 6x-4 (nog)(1) m(x) = 2x²-8x - 3 n(x) = 0.75x³-9 Start! 16 (jon)(2) 13 (km)(0) 7 (hog)(-1) 39 43 39 -34 -11 -31 19 (gok)(4) -95 (moj)(0) 22 (g° m)(5) 29 (joh)(-2) 13 46 -64 3 39 56 -6 (hoh)(11) 22 (kg)(-2) -59 (mon)(2) 37 (jok)(3) 0 11 5 -8 -12 36 32 (hom)(6) -16 (gon)(-2) -44 (ko j)(1) -20 End! C: Gina Wilson (All Things AlgebraⓇ, LLC), 2016

Profit A wholesaler sells graphing calculators. For an order of x calculators his total cost in dollars is C=50+30x0.1x2 and his total revenue is R=50x0.05x2 a Find the profit P on an order of x calculators. b Find the profit on an order of 10 calculators and on an order of 20 calculators.

Applications Waste management The corrosive waste is industrial sewage limits the useful life of the piping in a waste processing plant to 12 years. The piping system was originally worth 137,000, and it will cost the company 33, 000 to remove it at the end of its 12-year useful life. Find a depreciation equation.

Find the dimensions of the rectangular corral splitinto 2 pens of the same size producing the greatestpossible enclosed area given 300 feet of fencing.

Height of a basketball The path of a basketball thrown from the free throw line can be modeled by the quadratic function f(x)=0.06x2+1.5x+6, where x is the horizontal distance in feet from the free throw line and f(x) is the height in feet of the ball. Find the maximum height of the basketball.

Graph: 3x+2y6.

Among all of the pairs of numbers whose differenceis 12, find the pair with the smallest product. Whatis the product?

The graph of a quadratic function is shown on the grid.       Which function is best represented by this graph?     f (x)=  −12x2 + 16 ⊝     f (x)=  −x2 + 16 ⊝     f (x)=  −12x2 + 8 ⊝     f (x)=  −x2 + 8 ⊝ CLEAR ALL       ❮PREVIOUS

A. Projectile Motion A child throws a ball upward from the roof of a house. The trajectory is parabolic, according to the laws of physics. The height of the ball above the ground, h(x) (in meters) is given by the quadratic function: h(x) = -3x2 + 6x + 4 where x is the horizontal distance from the house in meters. The goal of this tutorial is to graph this function and analyze and interpret the graph within the problem context. Show the following steps on the blackboard or paper as your instructor directs: a) State the coordinates of the h-intercept. Explain the meaning of this intercept within the problem context. b) Complete the square on the right-hand side to convert the function from general form to standard form. State the coordinates of the vertex. c) Find vertex by using the vertex formula. The result should be the same as in part b) above.

A. Projectile Motion A child throws a ball upward from the roof of a house. The trajectory is parabolic, according to the laws of physics. The height of the ball above the ground, h(x) (in meters) is given by the quadratic function: h(x) = -3x2 + 6x + 4 where x is the horizontal distance from the house in meters. The goal of this tutorial is to graph this function and analyze and interpret the graph within the problem context. Show the following steps on the blackboard or paper as your instructor directs: d) What is the significance of the vertex in this problem context? e) Using all of the information from parts a) through d), sketch the quadratic function on its mathematical domain. Scale your graph appropriately and label all the important parts of the trajectory. f) Identify the practical domain on your graph and state the practical domain in interval notation. g) Use the quadratic formula to find the x-intercepts. Simplify fully and express exact answers. Plot these points on your…