Exercises: Relate the Domain of a Function to Its Graph and Quantitative Context

$( 3, \infty )$

$[ 3, \infty )$

$( -\infty, 3 ]$

$( -\infty, 3 )$

$f(x) = 3x - 7$

$g(x) = x^2 + 4$

$h(x) = \dfrac{1}{x + 2}$

$k(x) = |x| + 1$

The function is undefined for all $x$ near 3.

The point $( 3, 5 )$ is excluded — $x = 3$ is not in the domain.

The function has a vertical asymptote at $x = 3$.

The output at $x = 3$ is zero.

$( -\infty, 4 ) \cup ( 4, \infty )$

$( -\infty, \infty )$

$( 4, \infty )$

$( -\infty, 4 ]$

$( -\infty, \infty )$

$( -\infty, 3 )$

$[ 3, \infty )$

$( 3, \infty )$

$[ -1, \infty )$

$( -\infty, \infty )$

$[ -1, 5 ) \cup ( 5, \infty )$

$( -1, 5 ) \cup ( 5, \infty )$

$( -2, 6 )$

$[ -2, 6 ]$

$\{ -2, 6 \}$

$( -\infty, \infty )$

Draw a solid line through the origin with slope 3.

Draw isolated dots at $n = 0, 1, 2, 3, 4$.

Draw a ray starting at the origin extending to the right.

Draw a solid line from $( 0, 0 )$ to $( 4, 12 )$.