a function is graphed on a coordinate grid. as the domain values approach infinity, the range values…

a function is graphed on a coordinate grid. as the domain values approach infinity, the range values approach infinity. as the domain values approach negative infinity, the range values approach negative infinity. to which family of functions might the described function belong?\nabsolute value\nexponential\ncube root\nsquare root

a function is graphed on a coordinate grid. as the domain values approach infinity, the range values approach infinity. as the domain values approach negative infinity, the range values approach negative infinity. to which family of functions might the described function belong?\nabsolute value\nexponential\ncube root\nsquare root

Answer

Brief Explanations:

  1. Analyze absolute - value function: The absolute - value function (y = |x|) has a range of (y\geq0). As (x\to\pm\infty), (y\to+\infty), not (y\to-\infty) as (x\to-\infty).
  2. Analyze exponential function: For an exponential function (y = a^x) ((a>0,a\neq1)), if (a > 1), as (x\to+\infty), (y\to+\infty) and as (x\to-\infty), (y\to0); if (0 < a<1), as (x\to+\infty), (y\to0) and as (x\to-\infty), (y\to+\infty). It does not satisfy the given behavior.
  3. Analyze cube - root function: The cube - root function (y=\sqrt[3]{x}) has a domain and range of all real numbers. As (x\to+\infty), (y\to+\infty) and as (x\to-\infty), (y\to-\infty), which satisfies the given conditions.
  4. Analyze square - root function: The square - root function (y = \sqrt{x}) has a domain of (x\geq0) and a range of (y\geq0), so it cannot have values as (x\to-\infty).

Answer:

cube root