MAT 103B Practice Final

Key

No Calculators Portion

Problem 1.  Use transformations to sketch the graph.  Then state the domain and range.

A. 

B. 

Problem 2.  Find the domain of the function

Problem 3.  List the intercepts and test for symmetry

Problem 4.  Determine if the graph of the quadratic function is concave up or down, find the vertex, intercepts and axis of symmetry, and where the function is increasing and where it is decreasing.  Then use this information to sketch a graph of the function.

Problem 5.  List the real zeros, determine whether the function crosses or touches the x-axis at each intercept, determine the maximum number of turning points on the graph, determine the left and right behavior, then use the information to sketch a possible graph.

Problem 6.  Sketch the graph of the rational function.

Problem 7.  Use algebraic methods to find the roots of

Problem 8.  Form a polynomial with real coefficients having the given degree and zeros. 

Degree 7:  The only real zero is -3.  Complex zeros include 3i and 1+2i.

With Calculators Portion

Problem 9.  Find the distance between the point (5,1) and the maximum point on the graph of

Problem 10.  The data describes the amount spent x (in thousands of dollars) on advertising vs. revenue y  (in thousands of dollars)  for a business.  Determine whether a linear model or a quadratic model should be used.  Then find the equation for this model.  Use your equation to predict the revenue if a business spends $3000 on advertising.  If the model is linear, interpret the slope and y-intercept.

Problem 11.  A track and field playing area is in the shape of a rectangle with semicircles at each end.  The perimeter of the track is to be 1200 meters.  What should the dimensions of the rectangle be so that the area of the rectangle is a maximum?

Problem 12.  One of the vertices of a rectangle is at the origin.  Another is on the curve y = 4 - x² in the first quadrant.  Find the dimensions of the largest rectangle that can be constructed in this way.