Mr. Kone Math Hub · Review sheet

What Is a Function?

Unit 6: Functions & Function Notation · NY-8.F.1, NY-8.F.2, NY-8.F.5, AI-F.IF.1

Notes

One output, not one input. Two different inputs may share an output (y = x²). One input may not have two outputs. That is the vertical line test.

Vocabulary

• function: A relation in which each input has exactly one output.
• domain: The set of all possible inputs.
• range: The set of all possible outputs.

Practice (no calculator unless marked)

1. Which function has a domain of all real numbers and a range greater than or equal to three?
   • A. f(x) = 2x + 3
   • B. g(x) = x² + 3
   • C. h(x) = 3ˣ
   • D. m(x) = |x + 3|
2. A table of values represents a function. Which statement describes the function?
   • A. The function is nonlinear because the intercept is 0.
   • B. The function is linear because the rate of change is constant.
   • C. The function is linear because the intercept is a constant value.
   • D. The function is nonlinear because the rate of change is not constant.
3. Which set of ordered pairs represents a function?
   • A. {(−20, 30), (−40, 0), (−40, 50)}
   • B. {(−30, 0), (−30, 20), (−30, 50)}
   • C. {(−40, 0), (20, −30), (60, −50)}
   • D. {(−50, 0), (20, −30), (−50, 60)}
4. Which function has a domain of all real numbers and a range greater than or equal to three?
   • A. f(x) = 2x + 3
   • B. g(x) = x² + 3
   • C. h(x) = 3ˣ
   • D. m(x) = |x + 3|
5. A table of values represents a function. Which statement describes the function?
   • A. The function is nonlinear because the intercept is 0.
   • B. The function is linear because the rate of change is constant.
   • C. The function is linear because the intercept is a constant value.
   • D. The function is nonlinear because the rate of change is not constant.
6. Which set of ordered pairs represents a function?
   • A. {(−20, 30), (−40, 0), (−40, 50)}
   • B. {(−30, 0), (−30, 20), (−30, 50)}
   • C. {(−40, 0), (20, −30), (60, −50)}
   • D. {(−50, 0), (20, −30), (−50, 60)}
7. Which function has a domain of all real numbers and a range greater than or equal to three?
   • A. f(x) = 2x + 3
   • B. g(x) = x² + 3
   • C. h(x) = 3ˣ
   • D. m(x) = |x + 3|
8. A table of values represents a function. Which statement describes the function?
   • A. The function is nonlinear because the intercept is 0.
   • B. The function is linear because the rate of change is constant.
   • C. The function is linear because the intercept is a constant value.
   • D. The function is nonlinear because the rate of change is not constant.