Question

A. Give the equation of each vertical asymptote, and give the corresponding factor that will appear in the rational function.

vertical asymptote           factor

Should these factors appear in the numerator or denominator of function?

B. Give the x-intercept of the function, tell whether the graph crosses or touches the x-axis, give the corresponding factor that will appear in the rational function, and tell whether the power will be even or odd.

x-intercept         cross/touch                       factor                   odd/even power

Should these factors appear in the numerator or denominator of the function?

C. Using your information from A and B, form a trial function. Write that function below.

Now use your calculator to test it visually, setting your calculator so that the viewing window matches the grid of the graph.   Do you need to change any powers or multiply the numerator by -1 to make your graph look more like the one given? If so, make the necessary change(s) and show your modified function below.

Continue checking your function algebraically, as follows:

i)   What y-intercept does your function have?  

Is it the same as the y-intercept of graph given?

If not, modify your function to make them match (without changing the x-intercepts or the vertical asymptotes) and show the modified function below.

ii)   What is the horizontal asymptote for your function?

Does the graph given have the same horizontal asymptote?  

If not, modify your function to make them match (without changing the x-intercepts and the vertical asymptotes) and show the modified function below.

D. Write your final function here:

Answer 1

Sol Folom the 99aph we see that Value of function tends to infinity on .. at *=-3 and 4:3 veutical Asymptore | Factor 2+3 2-3 313-3 0=3 the these will appear in denominatog factools q- intercept!- the point where the graph touches y cut 2-axis at 7=1 Helle graph touching ar-cris na-integcept:-(1,0) Touch Factog- (2-1) poweg- even Numegatool these factors will appear in © f(n) = -(-135 (1+3)(x-3)