Polynomial & Rational Functions — Quiz 4

Questions in this quiz (8)

1. If $$f(x)=x^2-3$$, then $$f(a+2)=$$

   • $$a^2+2a-3$$
   • $$a^2+4a+1$$
   • $$a^2+4a+4$$
   • $$a^2+4a-1$$

2. If $$f(x)=x^2-3$$, then $$\frac{f(x+h)-f(x)}{h}=$$

   • $$2x+h$$
   • $$2x+2h$$
   • $$2x+h-3$$
   • $$x+h$$

3. A ball is thrown into the air such that its height, $$h$$, in feet at any time $$t$$, in seconds is given by the function $$h(t)=-16t^2+64t+5$$. What is the maximum height, in feet, attained by the ball?

   • $$69$$
   • $$53$$
   • $$37$$
   • $$5$$

4. If the function $$f$$ is defined by $$f(x)=2x+k$$ and the function $$g$$ is defined by $$g(x)=\frac{x+3}{2}$$, for what value of $$k$$ is $$f(g(x))=g(f(x))$$?

   • $$-3$$
   • $$0$$
   • $$3$$
   • $$k$$ does not exist

5. What is the equation of the function $$h(x)$$ whose graph can be obtained by transforming the graph of $$f(x)=\sqrt{x-2}+1$$ up $$3$$ units, followed by reflecting over the $$x$$-axis, followed by a horizontal stretch by a factor of $$2$$?

   • $$h(x)=-\sqrt{\frac{x}{2}-2}-4$$
   • $$h(x)=-\sqrt{2x-2}-4$$
   • $$h(x)=-\sqrt{\frac{x}{2}-1}-4$$
   • $$h(x)=-\sqrt{2x-1}-4$$

6. If $$f(x)=4x-3$$ and $$g(x)=\frac{x}{4}+k$$ are inverse functions, what is the value of $$k$$?

   • $$-3$$
   • $$\frac{3}{4}$$
   • $$\frac{1}{4}$$
   • $$3$$

7. If $$f(x)=\frac{3x+2}{x-1}$$, find the equation of its inverse, $$f^{-1}(x)$$.

   • $$\frac{x+2}{x-3}$$
   • $$\frac{x-2}{3-x}$$
   • $$\frac{x+1}{3-x}$$
   • $$\frac{x-1}{3-x}$$

8. Jordan buys a new outdoor grill. The cost for the unit is $$299.99$$ dollars. If the annual operating cost is $$98.50$$ dollars, which function models the total cost over the lifetime of the unit, $$C(t)$$, in terms of the number of years $$t$$?

   • $$C(t)=299.99+98.50t$$
   • $$C(t)=299.99t+98.50$$
   • $$C(t)=\frac{299.99+98.50}{t}$$
   • $$C(t)=299.99+9.85t$$