Functions, Graphs, Domains and Asymptotes
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Please refer to the attached file for the formatted homework problem set.
1. State the domain of the following:
a) f(x) = square root(x+4)
b) g(x) = (2x + 1) / (x - 7)
c) h(x) = 3x^2 + fx - 3
d) l(x) = 2x + 3
e) m(x) = 3 / (x^2 + 7)
2. Suppose the graph of y = x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph? Write your answers in terms of x^2 and/or x.
(see attached file)
3. Consider the following graph of y = f(x).
a) If h(x) = f(x) + 2, what would the new coordinates of P be after the shift? Give answer in (x, y) form.
b) If k(x) = f(-x), what would the new coordinates of P be after the reflection? Give answer in (x, y) form.
4. Consider the function f(x) = x^2 + 4x + 1.
a) Find h, the x-coordinate of the vertex of this parabola.
b) Substitute the two integers immediately to the left and right of h into the function to find the corresponding y. Fill in the following table. Make sure your x-values are in increasing order in your table.
c) Use MS Excel to graph the function by plotting the points found in the table in part b.
5. Find the equations of the horizontal and vertical asymptotes for the following. Type none if the function does not have an asymptote.
a) f(x) = (2x + 3) / (x + 2)
b) g(x) = 5x / (x^2 - 1)
c)
d)
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