Function concept and notation Knowledge-Based Download PDF

Questions

1. 1.

   A function $f$ satisfies the equation $f(x) + 3f(-x) = 4x + 8$ for all real numbers $x$. What is the value of $f(2)$?

   • A) $-4$
   • B) $-2$
   • C) $1$
   • D) $2$
2. 2.

   A real-valued function $f$ is defined by $f(x) = \frac{3x - 5}{x + 2}$ for all $x \neq -2$. If $f(m) = 4$, what is the value of $m$?

   • A) $-3$
   • B) $-13$
   • C) $\frac{7}{6}$
   • D) $13$
3. 3.

   Let $X = \{1, 2, 3, 4\}$ and $Y = \{a, b, c\}$. Which of the following sets of ordered pairs defines a function from $X$ to $Y$?

   • A) $\{(1, a), (2, b), (3, c)\}$
   • B) $\{(1, a), (2, b), (2, c), (3, a), (4, b)\}$
   • C) $\{(1, b), (2, b), (3, a), (4, c)\}$
   • D) $\{(1, a), (2, b), (3, c), (4, d)\}$
4. 4.

   Which of the following equations defines $y$ as a function of $x$ for all real numbers?

   • A) $x^2 + y^2 = 25$
   • B) $y^3 - 2x = 1$
   • C) $x = y^2 - 1$
   • D) $|y| = x + 4$
5. 5.

   If $f(2x + 1) = 4x^2 - 6x + 5$, what is the value of $f(5)$?

   • A) 75
   • B) 9
   • C) 17
   • D) 23