Polynomial & Rational Functions — Quiz 1

Questions in this quiz (10)

1. Which of the following functions has a domain of $$x\ge0$$?

   • $$f(x)=\frac{1}{x}$$
   • $$f(x)=\sqrt{x}$$
   • $$f(x)=\ln(x-2)$$
   • $$f(x)=\frac{1}{x-3}$$

2. Which of the following are functions?I. $$y+2x=10$$ II. $$x^2+y^2=25$$III. $$y=3x-4$$ IV. $$x=y^2-1$$

   • I and III only
   • I, II, and III
   • I, III, and IV
   • II and IV only

3. Find the average rate of change of $$f(x)=2x^2+3$$ from $$x=1$$ to $$x=5$$.

   • $$12$$
   • $$10$$
   • $$8$$
   • $$6$$

4. Which of the following linear functions is decreasing?

   • $$f(x)=3x+2$$
   • $$g(x)=5$$
   • $$h(x)=-2x+1$$
   • $$p(x)=0.5x-4$$

5. If $$a$$ represents the zero of the function $$f(x)=(x-4)^2$$, evaluate $$g(a)$$ if $$g(x)=6-(x-2)^2$$.

   • $$2$$
   • $$4$$
   • $$6$$
   • $$8$$

6. A bakery has daily fixed costs of $$85$$ dollars, and each cupcake costs $$1.25$$ dollars to make. Which of the following represents a model that expresses the cost, $$C$$, of baking $$n$$ cupcakes in a day?

   • $$C(n)=1.25n+85$$
   • $$C(n)=85n+1.25$$
   • $$C(n)=1.25x+85$$
   • $$C(n)=0.85n+12.5$$

7. For the function $$f(x)=2x^2-3x+4$$, evaluate $$f(x+h)$$.

   • $$2x^2-3x+4+h$$
   • $$2x^2+4xh+2h^2-3x-3h+4$$
   • $$2x^2+2h^2-3x-3h+4$$
   • $$2x^2+4xh-3x+4$$

8. Which of the following functions has the domain $$(-\infty,\infty)$$, $$x\ne-2$$, $$x\ne5$$?

   • $$f(x)=\frac{\sqrt{x+10}}{x+1}$$
   • $$g(x)=\frac{x}{(x+2)(x-5)}$$
   • $$h(x)=\frac{x}{x+2}$$
   • $$i(x)=x^2+3x-10$$

9. As a cup of coffee cools, the temperature is recorded in the table below, where $$t$$ is measured in minutes and temperature $$T(t)$$ is measured in degrees Fahrenheit. Using the data in the table, which of the following best approximates the rate at which the temperature is changing at time $$t=4$$?

   • $$-6$$ °F/min
   • $$-5.6$$ °F/min
   • $$-4.8$$ °F/min
   • $$-3.2$$ °F/min

10. Given the table of values below, which of the following best describes the behavior of the graph of the function in the interval $$1\le x\le6$$?

    • increasing, concave down
    • increasing, concave up
    • decreasing, concave down
    • decreasing, concave up