Domains & Equations of Functions
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1) State the domain of the following:
a) f(x) = sqrt (x - 8)
b) h(x) = 3x^2 + 5x - 3
c) m(x) = 5/(x^2 + 9)
d) l(x) = 5x - 4
e) g(x) = (7x + 4) / (x+4)
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?
3) Consider the following graph of y = f(x).
a) If h(x) = f(x) - 3, what would the new coordinates of P be after the shift? Give answer in (x, y) form.
b) If 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 + 6x - 2
a) Find h, the x-coordinate of the vertex of this parabola.
b) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y. Fill in the table below. 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 horizontal and vertical asymptotes of the following. Type "none" if the function does not have an asymptote.
a) f(x) = (2x -3)/(x^2 +2)
b) g(x) = 5x / (x -1)
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1) a) The variable under the square ...
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