Heart of Algebra: Linear Functions — Quiz 4

Questions in this quiz (10)

1. A linear function $$f$$ gives a company’s revenue, in dollars, from selling $$x$$ items. The revenue is $$180$$ when $$6$$ items are sold and $$300$$ when $$10$$ items are sold. Which equation defines $$f$$?

   • $$f(x)=30x$$
   • $$f(x)=30x-30$$
   • $$f(x)=30x+30$$
   • $$f(x)=30$$

2. The table shows a linear relationship. What is the $$x$$-intercept of the graph of $$y=f(x)$$?

   • $$(0,0)$$
   • $$(-6,0)$$
   • $$(6,0)$$
   • $$(-3,0)$$

3. The functions $$f$$ and $$g$$ are defined as $$f(x)=\frac{1}{2}x-4$$ and $$g(x)=\frac{1}{2}x+6$$. If $$h(x)=f(x)+g(x)$$, what is the $$x$$-intercept of $$y=h(x)$$?

   • -2

4. According to a model, the length, in centimeters, of a fish is given by adding $$2$$ to three times its age $$x$$, in years. What is the length of a fish that is $$4$$ years old?

   • 14

5. The function $$f$$ is defined by $$f(x)=3x+k(x-2)$$, where $$k$$ is a constant and $$f(4)=20$$. What is the value of $$f(8)$$?

   • 48

6. The boiling point of a liquid is $$150^\circ F$$ at sea level. For every $$300$$ feet above sea level, the boiling point decreases by $$2^\circ F$$. Which equation models the boiling point $$B$$, in $$^\circ F$$, at an elevation of $$x$$ feet?

   • $$B=150+\frac{2x}{300}$$
   • $$B=150-\frac{2x}{300}$$
   • $$B=300-\frac{2x}{150}$$
   • $$B=150-\frac{x}{150}$$

7. The function $$f(x)=48-0.2x$$ models the temperature of a liquid. What is the temperature when $$x=30$$?

   • $$42$$
   • $$48$$
   • $$6$$
   • $$-6$$

8. A table shows that $$1$$ unit equals $$3.5$$ meters and $$2$$ units equal $$7$$ meters. If $$x$$ units is equivalent to $$y$$ meters, which equation represents the relationship?

   • $$y=0.35x$$
   • $$y=3.5x$$
   • $$x=3.5y$$
   • $$xy=3.5$$

9. Maria saves $$\frac{3}{4}$$ of the $$120$$ dollars she earns each week. If she continues saving at this rate, how much money, in dollars, will Maria save in $$6$$ weeks?

   • 540

10. Which of the following is the graph of the equation $$y=-2x+3$$ in the $$xy$$-plane?

    • $$\text{A line with positive slope passing through }(0,3)$$
    • $$\text{A line with negative slope passing through }(0,3)$$
    • $$\text{A horizontal line at }y=3$$
    • $$\text{A vertical line at }x=3$$