Exercises

1. If {(1, 5), (2, 13), (x, y)} is a function, which of the following must be true?

   1. x > 2
   2. y ≠ 13
   3. x ≠ 1
   1. None
   2. I only
   3. II only
   4. III only
   5. I and II only

2. If $f\left(x\right)=-3x^3-3\sqrt[3]{x}$, what is the value of f(–8)?

   1. 78
   2. 1,530
   3. 1,542
   4. 13,818
   5. 13,830

3. What is the domain of the function $f\left(x\right)={\displaystyle \frac{{\left(x-2\right)}^3}{{\left(x+2\right)}^2}}$ ?

   1. All real numbers
   2. {x | –2 < x < 2}
   3. {x | x ≠ 2}
   4. {x | x ≠ –2}
   5. {x | x < –2 or x > 2}

4. If $f\left(x\right)=x+\frac{1}{x}$, what is f(f(x))?

   1. 1
   2. $x+\frac{1}{x}$
   3. $x^2+\frac{1}{x^2}$
   4. $\frac{x^2+1}{x}$
   5. $\frac{x^2+1}{x}+\frac{x}{x^2+1}$

5. Which of the following graphs is not the graph of a function?

   1. 

   2. 

   3. 

   4. 

   5. 

6. What is the range of the function $f\left(x\right)=\sqrt{x^2-4}$ ?

   1. All real numbers
   2. All real numbers greater than or equal to 0
   3. All real numbers greater than or equal to 2
   4. All real numbers greater than or equal to 2 or less than or equal to –2
   5. All real numbers between –2 and 2, inclusive

7. Which of the following is not the equation of a function?

   1. y = 3
   2. x = 3
   3. y = x
   4. y = |x|
   5. $y=\frac{\left|x\right|}{x}$

8. 1. Question 8 and 9 refer to the following graphs. The first one is the graph of y = |x|.

      

      $y=f\left(x\right)=\left|x\right|$

   8. Which of the graphs is the graph of y = |x – 3|?

      1. Graph A
      2. Graph B
      3. Graph C
      4. Graph D
      5. Graph E

   9. Which of the graphs is that of y = ||x|–3|?

      1. Graph A
      2. Graph B
      3. Graph C
      4. Graph D
      5. Graph E

   

   (A)

   

   (B)

   

   (C)

   

   (D)

   

   (E)

10. If x ≠ 1, 2, f(x) = x² – 1, g(x) = x² – 4, and h(x) = x² – 3x + 2, then $\left(\frac{fg}{h}\right)\left(x\right)=$

    1. x² + 3x + 2
    2. x² – 3x + 2
    3. x⁴ – 4
    4. $\frac{x^4+4}{x^2-3x+2}$
    5. $\frac{x^2+4}{-3x+2}$

11. If f(x) = x² – 1 and g(x) = x² + 1, what is (f ⚬ g)(x) – (g ⚬ f)(x)?

    1. –2
    2. 0
    3. x⁴ – 1
    4. 4x²
    5. 4x² – 2

12. If $f\left(x\right)=\frac{4-3x}{2}$, then f^–1(x) =

    1. $\frac{4-2x}{3}$
    2. $\frac{3x-4}{2}$
    3. $\frac{2x-4}{3}$
    4. $\frac{2-3x}{4}$
    5. $\frac{3x-2}{4}$