MATHEMATICS HIGH SCHOOL

Which statement describes the behavior of the function f(x)=3x/4-x?a. The graph approaches –3 as x approaches infinity.
b. The graph approaches 0 as x approaches infinity.
c. The graph approaches 3 as x approaches infinity.
d. The graph approaches 4 as x approaches infinity.

Answers

Answer 1

Answer:

Answer:

The graph approaches –3 as x approaches infinity. Option a is correct.

Step-by-step explanation:

The given function is

$f(x)=(3x)/(4-x)$

We have to find value of function as x approaches infinity. Take limit both sides as x approaches to infinity.

$\lim_(x\rightarrow \infty)f(x)=\lim_(x\rightarrow \infty)(3x)/(4-x)$

Taking x common from the denominator.

$\lim_(x\rightarrow \infty)f(x)=\lim_(x\rightarrow \infty)(3x)/(x((4)/(x)-1))$

Cancel out common factor x.

$\lim_(x\rightarrow \infty)f(x)=\lim_(x\rightarrow \infty)(3)/((4)/(x)-1)$

Apply limits.

$\lim_(x\rightarrow \infty)f(x)=(3)/((4)/(\infty)-1)$

$\lim_(x\rightarrow \infty)f(x)=(3)/(0-1)$

$\lim_(x\rightarrow \infty)f(x)=-3$

Therefore the graph approaches –3 as x approaches infinity.

Answer 2

Answer: a. The graph approaches –3 as x approaches infinity.

$f(x) = (3x)/(4-x) +3 -3 = (3x+12-3x)/(4-x) -3 = (12)/(4-x) -3$

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