Function concept and notation Knowledge-Based Practice

Math · Functions & Trigonometry · Math · Function Fundamentals

5 Math practice questions on Function concept and notation. Questions that assess core concepts and understanding.

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Questions

1.
What is the domain of the real-valued function $f(x) = \sqrt{6 - 2x} + \frac{1}{\sqrt{x + 4}}$ ?
- A) $[-4, 3]$
- B) $(-4, 3)$
- C) $[-4, 3)$
- D) $(-4, 3]$
2.
A function $f$ defined on the set of real numbers satisfies the relation $f(x) + 2f(-x) = 3x + 6$ for all real numbers $x$ . What is the value of $f(4)$ ?
- A) 14
- B) -2
- C) 6
- D) -10
3.
Which of the following equations defines $y$ as a real-valued function of $x$ for all real numbers $x$ ?
- A) $x^2 + y^2 = 25$
- B) $x = |y| + 2$
- C) $y^3 - 3x = 8$
- D) $x = y^2 - 1$
4.
A function is defined by $f(x) = 3x - 2$ for all real numbers $x$ . Which of the following expressions represents $f(2x + 1)$ in terms of $f(x)$ ?
- A) $2f(x) + 5$
- B) $2f(x) + 1$
- C) $2f(x) - 1$
- D) $2f(x) + 3$
5.
A function $f$ satisfies the equation $f(2x - 3) = 4x^2 - 10x + 7$ for all real numbers $x$ . What is the value of $f(5)$ ?
- A) 1
- B) 19
- C) 31
- D) 57

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