Heart of Algebra: Linear Functions — Quiz 3

Questions in this quiz (10)

1. The function $$f(x)$$ is defined as $$12$$ more than $$3$$ times a number $$x$$. If $$y=f(x)$$ is graphed in the $$xy$$-plane, what is the best interpretation of the $$x$$-intercept?

   • $$\text{When the number is }0,\ f(x)=12$$
   • $$\text{For each increase of }1\text{ in }x,\ f(x)\text{ increases by }3$$
   • $$\text{For each increase of }3\text{ in }x,\ f(x)\text{ increases by }12$$
   • $$\text{When }f(x)=0,\text{ the number is }-4$$

2. The equation $$h=\frac{9}{5}(v-273)+32$$ gives the corresponding temperature $$h$$, in degrees Fahrenheit, for a temperature $$v$$ kelvins. If a substance has a temperature of $$212$$ degrees Fahrenheit, what is the corresponding temperature, in kelvins?

   • 373

3. Scientists use the model $$y=0.5x+10$$ to predict the number of fish in a lake, where $$x$$ is time in months. If $$x=40$$, which of the following is closest to the predicted number of fish?

   • $$20$$
   • $$30$$
   • $$40$$
   • $$50$$

4. For the linear function $$h$$, the graph of $$y=h(x)$$ passes through the points $$(2,10)$$ and $$(4,14)$$. Which equation defines $$h$$?

   • $$h(x)=2x+6$$
   • $$h(x)=3x+4$$
   • $$h(x)=4x+2$$
   • $$h(x)=5x$$

5. For the linear function $$f$$, what is the value of $$a-b$$ if $$f(x)=ax+b$$?

   • $$-12$$
   • $$-8$$
   • $$8$$
   • $$28$$

6. A function is defined by $$f(x)=-3x+24$$, where $$f(x)$$ represents the amount of water, in liters, remaining after filling $$x$$ containers. Which statement best interprets the $$y$$-intercept?

   • $$3\text{ liters are removed per container}$$
   • $$\text{There were }24\text{ liters before filling any containers}$$
   • $$\text{Each container holds }24\text{ liters}$$
   • $$24\text{ containers were filled}$$

7. If $$f(x)=2x+5$$ and $$g(x)=4x$$, what is the value of $$3f(3)-g(3)$$?

   • $$9$$
   • $$15$$
   • $$21$$
   • $$27$$

8. For the linear function $$f$$, if $$h(x)=f(x)+2$$, which equation defines $$h$$?

   • $$h(x)=5x+5$$
   • $$h(x)=5x+7$$
   • $$h(x)=5x+15$$
   • $$h(x)=5x+17$$

9. Which of the following best describes the graph of $$y=4x-2?$$

10. A table shows that $$3$$ tickets cost $$24$$ dollars and $$6$$ tickets cost $$48$$ dollars. Which equation represents the cost $$c,$$ in dollars, of $$t$$ tickets?

    • $$c=8t$$
    • $$c=4t$$
    • $$c=12t$$
    • $$c=t+8$$