MAT 150 College Algebra Spring 2018 Test #6 Calculator Version NAME: KEY Calculator Type: TI-83 Plus USE YOUR CALCULATOR to do the following problems on this part of the quiz. 1. Use a graphing utility to Graph the following equation: (y^{2}-x^{2}=9). Show me your input and a sketch of what you see on your calculator including the picture window you used. [y^{2}-x^{2}=9] [y_{1}=\sqrt{x^{2}+9}] [y_{2}=-\sqrt{x^{2}+9}] 2. Use a graphing utility to help you solve the equation: (-4x=x+5). Show me your input and a sketch of what you see on your calculator including the picture window you used. [y_{1}=x^{3}-4x-\frac{1}{3}x-5] [x\approx2.514] 3. Given the rational function, (h(x)=\frac{x^{3}-16x}{x^{2}+9}), do the following items: A) Use your calculator to graph the function. Show me your input and a sketch of what you see on your calculator including the picture window you used. [y_{1}=\frac{(x^{3}-16x)}{(x^{2}+9)}] B) Use your calculator to help you find the LOCAL EXTREMA of the function. Approximate your values to three decimals. LOCAL MAX at: (-1.767, 1.877) LOCAL MIN at: (1.767, -1.877) C) Determine the interval(s) where the function is increasing. [(-\infty,-1.767)\cup(1.767,\infty)] 5. Let P be any point on the graph of (y=x^{3}.) A) Find a function that represents the distance from P on the graph of (y=x^{3}) to the point (0,3) as a function of x. You do not need to simplify your answer at all. [P(x,y)] [D=\sqrt{(x-0)^{2}+(y-3)^{2}}] [D(x)=\sqrt{x^{2}+(x^{3}-3)^{2}}] B) Use your calculator to graph the Distance function. Show me your input and a sketch of what you see on your calculator including the picture window you used. [y_{1}=\sqrt{(x^{2}+(x^{3}-3)^{2})}] C) What value(s) of x creates the smallest distance? Approximate your value(s) to three decimals. [x\approx1.403] 6. All of this is in Quadrant I. A rectangle has one corner on the graph of (y=16-x^{2},) another corner at the origin, another on the positive x-axis, and the last corner on the positive y-axis as shown in the figure below. A) Find the area, A, of this rectangle, as a function of x. [A=lw] [A(x)=(16-x^{2})x] [A(x)=16x-x^{3}] B) Use your calculator to graph the Area function. Show me your input and a sketch of what you see on your calculator including the picture window you used. [y_{1}=16x-x^{3}] C) What value(s) of x creates the largest area? Approximate your value(s) to three decimals. [x\approx2.309] MAT 150 College Algebra Spring 2018 Test #6 Calculator Version NAME: KEY Calculator Type: TI-83 Plus USE YOUR CALCULATOR to do the following problems on this part of the quiz. 1. Use a graphing utility to Graph the following equation: (x^{2}-y^{2}=16). Show me your input and a sketch of what you see on your calculator including the picture window you used. [x^{2}-y^{2}=16] [y^{2}=x^{2}-16] [y=\pm\sqrt{x^{2}-16}] 2. Use a graphing utility to help you solve the equation: (x^{3}-2x=x-2). Show me your input and a sketch of what you see on your calculator including the picture window you used. [y=x^{3}-2x-x+2] [y=x^{3}-3x+2] [x\approx-1.881] 3. Given the rational function, (h(x)=\frac{16x-x^{3}}{x^{2}+9}), do the following items: A) Use your calculator to graph the function. Show me your input and a sketch of what you see on your calculator including the picture window you used. [y=\frac{(16x-x^{3})}{(x^{2}+9)}] B) Use your calculator to help you find the LOCAL EXTREMA of the function. Approximate your values to three decimals. LOCAL MAX: (1.767, 1.877) LOCAL MIN: (-1.767, -1.877) C) Determine the interval(s) where the function is increasing. [(-1.767, 1.767)]