Consider the function holes.jpg  a) State the x-coordinate corresponding to any holes in the graph. You only need to give the x-value(s). If there is no hole in the graph, type “none”. Hole when x = [BLANK-1] b) Type the equation(s) of any vertical asymptote(s) for the graph of f(x).  Vertical asymptote(s): [BLANK-2] c) Type the equation of any horizontal asymptote for the graph of f(x). Horizontal asymptote: [BLANK-3] You are NOT required to show work for this problem.

Select all functions in the list below that are polynomials. You do NOT need to show work for this problem. 

You ARE required to show supporting work for this problem. Consider the rational function below:graph rational.PNG a) The graph of this function has vertical asymptote: [BLANK-1] b) The function has x-intercepts: [BLANK-2] c) The equation of the slant asymptote for the graph of this function is: [BLANK-3] d) Sketch the graph of the function on your paper. Please try to graph the following features as accurately as possible: vertical asymptote slant asymptote x- and y-intercepts

Match the equation of the rational function with its graph. You do not need to sketch these graphs by hand, just use clues from the equations such as asymptotes and intercepts.  You are NOT required to show work for this problem.

Consider the polynomial function below: graph poly.jpg  a)  The degree of the polynomial is: [BLANK-1] b) The x-intercept(s) where the graph crosses the x-axis is/are: [BLANK-2] c) The x-intercept(s) where the graph touches the x-axis and turns around is/are: [BLANK-3] d)  Sketch the graph on your paper and label the question number. Your sketch of the graph is the only thing that you are required to write down for this question. When I grade the graphs, I will be looking for: x-intercepts that are accurately plotted correct behavior of the graph at each intercept as described in parts b and c correct end behavior. 

Use long division to divide:  long division A.jpg  The quotient is: [BLANK-1] The remainder is: [BLANK-2] NOTE: You should type your answers in the blanks above as something like x^3 + x^2 + 1. However, you are also required to show your work for this problem. Please clearly label the problem number. You should scan and upload your work after you have completed all of the problems on this exam.

You ARE required to show work for this question.  Use synthetic division to state the quotient and remainder: synth div.jpg Quotient: [BLANK-1] Remainder: [BLANK-2] 

A sample from a patient is prepared using the Gomori methenamine silver stain. What type of microbe is suspected of being present?

Observations In the next section, you will be given one or two clips and a question. Listen and/or watch carefully and answer the question. 

Partial R code and the output is provided below, fill in the blanks in the code.vector_1