Functions, Domain, and Range Review

Flashcards testing concepts of relations, functions, vertical line test, domain, and range for continuous, discrete, quadratic, exponential, and linear graphs.

What condition must a relation meet in order to be classified as a function?

Every input must have exactly one output.

What graphical test is used to determine if a graph represents a function?

The Vertical Line Test (VLT).

What are the domain and range of the relation $\{(-6, 4), (5, -1), (0, 3), (-2, 4)\}$?

Domain: $\{-6, -2, 0, 5\}$; Range: $\{-1, 3, 4\}$

Why is a relation not a function if an input like $0$ maps to two different outputs?

Because a function requires every input to have exactly one output.

What are the domain and range of a continuous quadratic graph with a maximum output value at $y = 2$?

Domain: All real numbers ($-\infty < x < \infty$); Range: $y \le 2$ (All real numbers less than or equal to $2$)

What are the domain and range of a continuous exponential graph with a horizontal asymptote at $y = -5$?

Domain: All real numbers ($-\infty < x < \infty$); Range: $y > -5$ (All real numbers greater than $-5$)

What are the domain and range of a discrete relation with ordered pairs defined by inputs $\{-2, -1, 0, 1, 2\}$ and outputs $\{-8, 1, 4\}$?

Domain: $\{-2, -1, 0, 1, 2\}$; Range: $\{-8, 1, 4\}$

What are the domain and range of a continuous exponential graph with a lower boundary asymptote at $y = 0$?

Domain: All real numbers ($-\infty < x < \infty$); Range: $y > 0$ (All real numbers greater than zero)

What are the domain and range of a vertical line graph located at $x = 2$?

Domain: $x = 2$; Range: All real numbers

What are the domain and range of a continuous graph bounded by $-2 \le x \le 5$ and $-4 \le y \le 4$?

Domain: All real numbers greater than or equal to $-2$ AND less than or equal to $5$ ($-2 \le x \le 5$); Range: All real numbers greater than or equal to $-4$ AND less than or equal to $4$ ($-4 \le y \le 4$)

What are the domain and range of a continuous graph bounded by $-1 \le x \le 6$ and $-3 \le y \le 5$?

Domain: All real numbers greater than or equal to $-1$ AND less than or equal to $6$ ($-1 \le x \le 6$); Range: All real numbers greater than or equal to $-3$ AND less than or equal to $5$ ($-3 \le y \le 5$)

What are the domain and range of a graph bounded by $-2 \le x < 5$ and $-2 \le y \le 3$?

Domain: All real numbers greater than or equal to $-2$ AND less than $5$ ($-2 \le x < 5$); Range: All real numbers greater than or equal to $-2$ AND less than or equal to $3$ ($-2 \le y \le 3$)

What are the domain and range of an open-ended graph defined by $x > -3$ and $y > 1$?

Domain: All real numbers greater than $-3$ ($x > -3$); Range: All real numbers greater than $1$ ($y > 1$)