Heart of Algebra: Linear Functions — Quiz 1

Questions in this quiz (9)

1. For the linear function $$f(x)=5x+b$$, $$b$$ is a constant and $$f(6)=23$$. What is the value of $$b$$?

   • $$-7$$
   • $$-5$$
   • $$-3$$
   • $$3$$

2. A spring has length $$\ell=20+3w$$, where $$\ell$$ is the length in centimeters and $$w$$ is the weight in newtons. Which of the following describes the meaning of the $$3$$ in this context?

   • The length of the spring with no weight attached
   • The increase in the length, in centimeters, for each one-newton increase in weight
   • The weight needed to stretch the spring to 20 cm
   • The total length of the spring after 3 newtons are added

3. The table shows the number of hours $$h$$ of labor and the total charge $$f(h)$$, in dollars. There is a linear relationship between $$h$$ and $$f(h)$$. Which equation represents this relationship?

   • $$f(h)=40h+100$$
   • $$f(h)=50h+80$$
   • $$f(h)=20h+140$$
   • $$f(h)=60h+60$$

4. For the linear function $$g$$, the table shows values of $$x$$ and their corresponding values of $$g(x)$$. The function can be written as $$g(x)=mx+b$$. What is the value of $$b$$?

   • $$21$$
   • $$24$$
   • $$27$$
   • $$33$$

5. Water usage in a town decreased from $$5$$ million gallons in year $$0$$ to $$2$$ million gallons in year $$6$$. Assuming a constant rate of decrease, which function best models the water usage $$f(t)$$, in millions of gallons, $$t$$ years after year $$0$$?

   • $$f(t)=-\frac{1}{2}t+5$$
   • $$f(t)=-\frac{1}{3}t+5$$
   • $$f(t)=\frac{1}{2}t+5$$
   • $$f(t)=\frac{1}{3}t+5$$

6. A gym charges $$20$$ dollars per month plus a one-time registration fee of $$15$$. Which equation represents the total cost $$c$$, in dollars, after $$m$$ months?

   • $$c=20(m+15)$$
   • $$c=15(m+20)$$
   • $$c=20m+15$$
   • $$c=15m+20$$

7. The function $$f$$ is defined by $$f(x)=-4x+12$$. What is the y-coordinate of the $$y$$-intercept of the graph of $$y=f(x)$$?

   • 12

8. Hydrogen is placed inside a container and kept at a constant pressure. The graph shows the estimated volume, $$y$$, in liters, of the hydrogen when its temperature is $$x$$ kelvins. What is the estimated volume, in liters, of the hydrogen when its temperature is $$500$$ kelvins?

   • $$0$$
   • $$\frac{7}{500}$$
   • $$7$$
   • $$\frac{500}{7}$$

9. The graph of the linear function $$y=f(x)+19$$ is shown. If $$c$$ and $$d$$ are positive constants, which equation could define $$f$$?

   • $$f(x)=-d-cx$$
   • $$f(x)=d-cx$$
   • $$f(x)=-d+cx$$
   • $$f(x)=d+cx$$