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A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values negative infinity, the range values approach infinity. To which family of functions might the described functions belong?

Areciprocal
Bsquare root
Cexponential
Dquadratic

Verified Answer :

lolnah

d. Quadratic :)

i am taking the test so if I'm wrong I'll change my answer

isyllus

Answer:

D) Quadratic

Step-by-step explanation:

A function is graphed on a coordinate grid.

  • As the domain values approach infinity, the range values approach infinity.

       Domain: If \(x\rightarrow \infty\) then

       Range: \(y\rightarrow \infty\)

  • As the domain values negative infinity, the range values approach infinity.

       Domain: If \(x\rightarrow -\infty\) then

       Range: \(y\rightarrow \infty\)

We need to choose correct option which follows given domain and range.

Only quadratic function will follow the rule because it has even degree polynomial.

Quadratic function: \(f(x)=ax^2+bx+c\)

Degree = 2 and leading coefficient is positive.

Domain: \(x\belong (-\infty,\infty)\)

Range: \(y\belong (b,\infty)\)

Hence, D is correct option.

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