Reference no: EM131073316
1. Find the domain of the following functions:
f(x) = x2/x2-5x+4,
x3-x/√(x-4), x < 5;
g(x) =
100, x ≥ 10.
2. Sketch a graph of the following functions:
x2, x ≥ 0;
f(x) =
-x2, x < 0
g(x) = |2x2 - x -15|.
Specify whether each function is even , odd, or neither. Write down the intervals in which each function is increasing.
3. Sketch the following graphs:
f1(x) = sinx, f2(x) = sin(x - π/2), f3(x) = sin(x - π/2) + 3
and
g1(x) = ex, g2(x) = ex-2, g3(x) = ex-2 + 3.
4. Graph the ellipse (x-1)2 + 9(y-2)2 = 1. Use the vertical line test to see if the curve is the graph of a function.
5. Let f(x) = sinx and g(x) = log2x. Write out f o g and g o f and the domains of these compositions.
6. Solve the following equations for x:
i) log2(x+3) - log4(x+3) = 2;
ii) 3x2 = 94x.
7. Let f(x) = ln(2+x3). Find f-1(y). Write down the domain of f and f-1.
8. Simplify the expression sin(cos-1x), x ∈ (-1, 1).
9. Given that limx→0 sinx/x =1. Evaluate limx→0 sinπx/x.
10. Given the graph of f below. Determine limx→-∞f(x), limx→0-f(x), limx→0+f(x), limx→0 f(x), limx→1-f(x), limx→1+f(x), limx→1f(x), limx→2f(x), limx→3-f(x), limx→3+f(x), limx→3f(x), limx→∞f(x).
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