Task Sets: Relate domain to graph and context - Common Core Math - HS Functions

Work through problems with immediate feedback

Concepts

Which statement best describes the natural domain of a function?

The set of all real numbers that produce a positive output

The set of all real numbers for which the function's rule produces a defined output

The set of all real numbers between the smallest and largest output values

The set of all real numbers, since every formula accepts any input

The function $f(x) = \dfrac{4}{x - 3}$ is undefined at exactly one
real number. Enter that value of $x$ .

A graph shows a curve that extends continuously from $x = -4$ (solid
dot) to $x = 7$ (open circle). What is the domain of this function?

$(-4,\, 7)$

$[-4,\, 7]$

$[-4,\, 7)$

$(-\infty,\, \infty)$

The function $T(t) = 25 - 3t$ gives temperature in °C at time $t$
hours. At $t = 10$ , the output is $T(10) = -5$ °C.
Is $t = 10$ in the domain of $T$ ?

No — the output is negative, so $t = 10$ is not a valid input

Yes — the formula produces a defined real-number output at $t = 10$

No — time cannot be 10 because the temperature goes below zero

It depends on whether the temperature scale allows negative values

Procedures

The natural domain of $h(x) = \sqrt{2x - 6}$ is $[a, \infty)$ for
some real number $a$ . Enter the value of $a$ .

The function $f(x) = \dfrac{\sqrt{x + 1}}{x - 5}$ has two types of
restrictions. Which of the following correctly states its natural domain?

$x \geq -1$ and $x \neq 5$ , written $[-1,\, 5) \cup (5,\, \infty)$

$x > -1$ and $x \neq 5$ , written $(-1,\, 5) \cup (5,\, \infty)$

All reals except $x = 5$ , written $(-\infty,\, 5) \cup (5,\, \infty)$

$x \geq 0$ and $x \neq 5$ , written $[0,\, 5) \cup (5,\, \infty)$

A function $f$ is graphed. The graph consists of exactly five isolated
points at $x$ -values $1,\, 3,\, 5,\, 7,$ and $9$ (no other points).
What is the domain of $f$ ?

$[1,\, 9]$

$\{1,\, 3,\, 5,\, 7,\, 9\}$

All odd integers from 1 to 9

$[1,\, 9]$ restricted to odd integers

A graph shows a curve with a vertical asymptote at $x = 2$ and
no other restrictions. Using interval notation, what is the domain?

$(-\infty,\, 2]$

$(-\infty,\, 2) \cup (2,\, \infty)$

$(-\infty,\, \infty)$

$[2,\, \infty)$

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HSF.IF.B.5 Tutor Intake — Domain Restrictions, Graphs, and Context

Concepts

Procedures