Question

As x approaches infinity, for which function does f(x) also approach infinity? Select all that apply.

Answer 1

As x approaches infinity, the functions f(x) that also approach infinity are (a)
`\(12x^3\)`, (c)
`\(4x^3\)`, (e)
`\(0.2x^5\)`, and (f)
`54x^5`. These behaviors are determined by the leading terms in each function.

To determine which function approaches infinity as x approaches infinity, we can analyze the leading terms of each function, as they dominate the behavior for large values of x.

a.
`\(f(x) = (4x + 1)(3x + 5)(x-2)\)`

Leading term:
`\(4x \cdot 3x \cdot x = 12x^3\)`

As x approaches infinity, f(x) also approaches infinity.

b.
`\(f(x)=-4.8x(2x+3)(x-9)(x+5)\)`

Leading term:
`\(-4.8x \cdot 2x \cdot x = -9.6x^3\)`

As x approaches infinity, f(x) approaches negative infinity.

c.
`\(f(x)=(4x+3)(x-5)(x+8)(x-3)\)`

Leading term:
`\(4x \cdot x \cdot x = 4x^3\)`

As x approaches infinity, f(x) also approaches infinity.

d.
`\(f(x)=-0.5x(3x-7)(4x + 1)(x+9)(x-3)\)`

Leading term:
`\(-0.5x \cdot 3x \cdot 4x \cdot x = -6x^4\)`

As x approaches infinity, f(x) approaches negative infinity.

e.
`f(x)=0.2x(x+4)(x+7)(x+8)(x-2)(x-1)`

Leading term:
`\(0.2x \cdot x \cdot x \cdot x \cdot x = 0.2x^5\)`

As x approaches infinity, f(x) also approaches infinity.

f.
`\(f(x) = (9x-1)(3x+4)(2x-5)(x+8)(x-2)\)`

Leading term:
`\(9x \cdot 3x \cdot 2x \cdot x \cdot x = 54x^5\)`

As x approaches infinity, f(x) also approaches infinity.

Therefore, the functions that approach infinity as x approaches infinity are: a, c, e and f.

The probable question may be:

As x approaches infinity, for which function does f(x) also approach infinity? Select all that apply.

Select all that apply:

a. f(x) = (4x + 1)(3x + 5)(x-2)

b. f(x)= -4.8x(2x+3)(x-9)(x+5)

c. f(x)= (4x+3)(x-5)(x+8)(x-3)

d. f(x)= -0.5x(3x-7)(4x + 1)(x+9)(x-3)

e. f(x)= 0.2x(x+4)(x+7)(x+8)(x-2)(x-1)

f. f(x) = (9x-1)(3x+4)(2x-5)(x+8)(x-2)