Question

Which statement correctly describes the end behavior of f(x)=ax+b, where a and b are positive numbers?

Answer 1

Answer:

The correct option is 2.

Step-by-step explanation:

The given function is

$f(x)=ax+b$

Where, a and b are positive numbers.

The given function is the slope intercept form of a linear function. Where a is the slope and b is y-intercept.

Since slope is positive therefore function approaches to infinity as x approaches to infinity and function approaches to negative infinity as x approaches to negative infinity.

It is also proved by using limits.

$lim_{x\rightarrow \infty}f(x)=lim_{x\rightarrow \infty}(ax+b)$

Apply limits.

$lim_{x\rightarrow \infty}f(x)=a(\infty)+b=\infty$

Similarly,

$lim_{x\rightarrow -\infty}f(x)=lim_{x\rightarrow -\infty}(ax+b)$

Apply limits.

$lim_{x\rightarrow -\infty}f(x)=a(-\infty)+b=-\infty$

Therefore option 2 is correct.

$f(x)\rightarrow \infty \text{ as }x\rightarrow \infty$

$f(x)\rightarrow -\infty \text{ as }x\rightarrow -\infty$