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1.  Which of the following represents a sinusoidal curve with its highest point at \(y = 3\) and its lowest point at \(y = -1\)?

a.  \(f(x) = \sin(2x) + 2\)

b.  \(f(x) = 2\sin(x) + 1\).

c.  \(f(x) = 3\sin(x) + 1\).

d.  \(f(x) = 3\sin(x) + 2\).

e.  \(f(x) = \sin(3x) + 2\).

2.  Make a sketch of the graph \( y= f(x) = (x + 1)^2 - 4 \), and use it to find the range of \(f\).

a.  \( (-\infty, 2) \cup (2, \infty) \)

b.  \(x \neq 2\)

c.  \( (-\infty, -4] \)

d.  \( [-4, \infty)\)

e.  \( (\infty, \infty) \)

3.  Find the domain for \( g(x) = \frac{1}{x^2 - 2x} \).

a.  \( (-\infty, 0) \cup (2, \infty) \)

b.  \( (-\infty, 0] \cup [2, \infty) \)

c.  \([0, \infty) \)

d.  All reals except 0 and 2.

e.  \( (0, 2) \)

4.  Find the domain for \( h(x) = \frac{1}{\sqrt{x^2 - 2x}} \).

a.  \( (-\infty, 0) \cup (2, \infty) \)

b.  \( (-\infty, 0] \cup [2, \infty) \)

c.  \([0, \infty) \)

d.  All reals except 0 and 2.

e.  \( (0, 2) \)

5.  The inverse of \(f(x) = \frac{x}{2} - 1\)

a.  is \(f^{-1}(x) = 2x + 1\)

b.  is \(f^{-1}(x) = 2x - 1\)

c.  is \(f^{-1}(x) = 2x + 2\)

d.  is \(f^{-1}(x) = 2(x - 1)\)

e.  does not exist because the graph \(y = f(x)\) fails the horizontal line test.

6.  The inverse of \(f(x) = x^3\)

a.  is \(f^{-1}(x) = \frac{x}{3}\)

b.  is \(f^{-1}(x) = \sqrt[3]{x}\)

c.  is \(f^{-1}(x) = x^{-3}\)

d.  is \(f^{-1}(x) = x^3\)

e.  does not exist because the graph \(y = f(x)\) fails the horizontal line test.

7.  The inverse of \(f(x) = x^4\)

a.  is \(f^{-1}(x) = \frac{x}{4}\)

b.  is \(f^{-1}(x) = \sqrt[4]{x}\)

c.  is \(f^{-1}(x) = x^{-4}\)

d.  is \(f^{-1}(x) = x^4\)

e.  does not exist because the graph \(y = f(x)\) fails the horizontal line test.

8.  Let \(f(x) = x^2 + x + 2\) and \(g(x) = e^x\). Then

a.  \( (f\circ g)(x) = e^{2x} + e^x + 2\), \((g\circ f)(x) = e^{x^2 + x + 2}\)

b.  \( (f\circ g)(x) = e^{x^2 + x + 2}\), \((g\circ f)(x) = e^{2x} + e^x + 2\)

c.  \( (f\circ g)(x) = e^{x^2} + e^x + 2\), \((g\circ f)(x) = e^{x^2 + x + 2}\)

b.  \( (f\circ g)(x) = e^{x^2 + x + 2}\), \((g\circ f)(x) = e^{x^2} + e^x + 2\)