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 infinity. to which family of functions might the described function belong?\nreciprocal\nsquare root\nexponential\nquadratic

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 infinity. to which family of functions might the described function belong?\nreciprocal\nsquare root\nexponential\nquadratic

Answer

Brief Explanations:

  1. Analyze the behavior of each function type:
    • For reciprocal functions ($y = \frac{a}{x}$), as $x\rightarrow\pm\infty$, $y\rightarrow0$.
    • For square - root functions ($y=\sqrt{x}$ or its transformations), the domain is restricted (usually $x\geq0$ for the basic form) and the behavior as $x\rightarrow\pm\infty$ is not as described.
    • For exponential functions ($y = a^x$), as $x\rightarrow-\infty$, $y\rightarrow0$ (for $a > 1$) or $y\rightarrow\infty$ (for $0 < a<1$), which is not consistent with the given behavior.
    • For quadratic functions ($y = ax^{2}+bx + c$, $a\neq0$), when $a>0$, the parabola opens upwards. As $x\rightarrow\pm\infty$, $y\rightarrow\infty$.

Answer:

quadratic