Functions — Quiz 3

Questions in this quiz (10)

1. For the exponential function $$g$$, the value of $$g(2)$$ is $$k$$, where $$k$$ is a constant. Which of the following equivalent forms of the function $$g$$ shows the value of $$k$$ as the coefficient or the base?

   • $$g(x)=k\cdot b^{x-2}$$
   • $$g(x)=k^{x/2}$$
   • $$g(x)=a\cdot k^{x-2}$$
   • $$g(x)=k\cdot e^x$$

2. The height of water in inches, $$h$$, in a plant's water tank after $$w$$ weeks is given by the function below: $$h(w) = -\frac{1}{4}w + 30$$. Over a four-week period, by how much does the height of water in the tank change?

   • Increases by 1 inch
   • Increases by 4 inches
   • Decreases by 4 inches
   • Decreases by 1 inches

3. Which of these is the range of $$y = a \sin(bx + c) + d$$?

   • $$[d - a, d + a]$$
   • $$[d - b, d + b]$$
   • $$[a - d, a + d]$$
   • $$[a + d, a - d]$$

4. If $$y = \cos(bx)$$ has a period of $$\frac{3}{4}$$, what could the value of $$b$$ be?

   • $$\frac{\pi}{3}$$
   • $$\frac{\pi}{4}$$
   • $$\frac{8\pi}{3}$$
   • $$\frac{3\pi}{4}$$

5. If $$g(x) = x^2 + \frac{1}{x}$$, what is $$g(g(2))$$?

   • $$\frac{8}{36}$$
   • $$\frac{729}{36}$$
   • $$\frac{81}{4}$$
   • $$\frac{737}{36}$$

6. If $$f(x) = 4x + 3$$ and $$g(x) = 6x + b$$, for what real number $$b$$ does $$f(g(x)) = g(f(x))$$?

   • 3
   • 18
   • 15
   • 5

7. If $$f(a,b,c)=a^2b+bc^2$$, then find $$f(3,2,4)$$.

   • 50
   • 84
   • 96
   • 112

8. Consider the function: $$f(x)=\frac{(x-5)(x+4)}{(x-2)(x+3)(x+1)}$$ At what values of $$x$$ does the function have vertical asymptotes?

   • $$2,3$$
   • $$-4,2$$
   • $$-3,-1,2$$
   • $$3,-3,1$$

9. What is the range of the function: $$y=(x-1)^2+3$$

   • All real numbers
   • $$y \geq -3$$
   • $$y \geq 3$$
   • $$y\geq0$$

10. If $$f(x)=\frac{x}{2+x}$$, what is $$f(f(x))$$?

    • $$\frac{x}{4+3x}$$
    • $$\frac{x}{2+x}$$
    • $$\sqrt{\frac{x}{2+x}}$$
    • $$(\frac{x}{2+x})^2$$