MATH 110 Review EXAM 2

Jeopardy Old & New CombosLinesQuads Poly Want a Cracker Potpourri

Potpourri 100 Explain whether or not the table below represents a linear function: Answer: no; the rate of change is not constant. X12345 Y

Potpourri 200 Consider the polynomial function What is the degree of P(x)? State the end behavior of P(x) State the multiplicity of each zero Answer: degree 6 ; y →-∞ as x →±∞; -2 has multiplicity of 3, 4 has multiplicity of 2, and -5 has multiplicity of 1.

Potpourri 300 An airplane flies at 80 mph for the first third of a trip and then 120 mph for the rest of the trip. The entire trip is 400 miles. How long does the trip take? Answer: 3.75 hours

Potpourri 400 A restaurant’s profit P as a function of the number of meals served m is given by the equation State the intercepts and give a practical interpretation for each. What is the slope of this line? What does this number tell you about the profit? Answer: y-int (0,-200) means profit is -200 dollars; x-int (60,0) break-even point ; slope is (10/3) meaning every three meals served, the profit increases by 10 dollars.

Potpourri 500 A horticulturist has determined that the number of inches a young redwood tree grows in one year is a function of the annual rainfall r given by : What is the maximum number of inches a redwood can grow in one year? Answer: 13.5 inches.

Poly Want A Cracker 100 What is the smallest degree the polynomial could have? What is the sign of the leading coefficient? Answer: minimum degree 5 ; lead coefficient positive

Poly Want A Cracker 200 Find the equation of a polynomial function with the following information: 1.Negative lead coefficient 2.Even degree 3.Zeros at -3 (multiplicity 1), 0 (multiplicity 1), and 5 (multiplicity 2) Answer: y = -x(x+3)(x-5) 2

Poly Want A Cracker 300 What is the remainder for the following division: Answer: -x+15

Poly Want a Cracker 400 Consider the polynomial function Which of the following is/are true? 1.-2 is a zero of f(x) 2.x – 2 is a factor of f(x) 3.f(x) has only one real zero

Poly Want a Cracker 500 Solve the polynomial equation given below: Answer:

Quads 100 Find the equation of a quadratic with vertex (2,-1) and passing through the point (1,3). Answer:

Quads 200 Rewrite the quadratic function given in standard form: Answer:

Quads 300 Find the vertex and intercepts of the quadratic function given: Answer: V(-0.1,0.03) ; intercepts: ( ,0), (0.447,0) and (0, 29/1000)

Quads 400 A box is being constructed by cutting 2 inch squares from the corners of a rectangular piece of cardboard that is 6 inches longer than it is wide. If the volume of the box is to be 224 cubic inches, find the dimensions of the cardboard. Answer: 12 inches by 18 inches

Quads 500 A frame for a picture is 2 inches wide all around. The picture inside the frame is 4 inches longer than it is wide. If the area of the picture is to be 320 square inches, find the outside dimensions of the picture frame. Answer: 20 inches by 24 inches.

Lines 100 Write the equation of the line passing through (-2,2) and having a slope of Answer: y = -0.5x+1

Lines 200 Write the equation of the line containing the points (2,3) and (5,15) Answer: y = 4x-5

Lines 300 Fill in the table below so that the function is linear: Answer: the missing y values in order are 4 and The missing x values in order are 2 and x f(x)

Lines 400 Find k so that the line containing the points (-3,k) and (4,8) is parallel to the line containing the points (5,3) and (1,6). Answer: k = 13.25

Lines 500 On most state highways, the fine for speeding depends on the speed of the car. In a certain state where the speed limit is 65 mph, the fine for driving 70 mph is $30 and the fine for driving 85 mph is $90. Assuming this relationship is linear, find the equation of the line that expresses the fine as a function of the speed of the car. How fast do you need to be driving to be fined $110? Answer: Equation: y = 4x-250 ; 90 mph

Combos 100 Given the functions and State the domain of (f + g)(x) Answer: [4,∞)

Combos 200 Consider the functions and State the domain of (f/g)(x) Answer: (-2,0) U (2,0)

Combos 300 Consider the functions and Find Answer:

Combos 400 An accident at an oil drilling platform is causing a circular shaped oil slick to form. The volume of the slick is roughly given by where r is the radius of the slick in feet. At the same time, the radius of the slick increases according to the function where t is in minutes. Find V(r(t)) and give a practical interpretation How long until the volume of the slick is 226 cubic feet. Answer: V(r(t)) tells us the volume of the slick t minutes after it started. It takes about an hour for the slick to reach 226 cubic feet.

Combos 500 Find f(g(2)) and g(f(0)) given the tables below: Answer: 3 ; 1 xf(x)g(x)

Old & New 100 Given that (3,4) is a point on the graph of f(x), which of the following must a point on the graph of a)(-6, 2) b)(-6, 8) c)(-1.5, 2) d)(-1.5, 8)

Old & New 200 Write the equation of the base graph which has been transformed in the following ways: first, reflected over the x- axis, vertically compressed by one-third, shifted right 4 units. Answer:

Old & New 300 Consider the function. What is the equation of the graph that will compress the graph horizontally by a factor of 3, move the graph left 2 units and reflect the graph over the x-axis (in that order). Answer:

Old & New 400 Suppose that a function f(x) has a domain of [-6,4]. What will the domain be for the function ? Answer: [-16,14]

Old & New 500 Suppose that a function f(x) has a range of [-2,1]. What will the range be for the function ? Answer: [3,9]