Question

Which statement describes the end behavior of the exponential function f(x) = 2x – 3?

Answer 1

The correct answer is:

As x→-∞, y→-3.
As x→∞, y→∞.

Explanation:

As our values of x get further into the negative numbers, the value of 2ˣ will approach 0. This is because raising a number to a negative exponent "flips" the number below the denominator and raises it to a power; we end up with smaller and smaller fractions, eventually so small that they nearly equal 0.

This will make the value of the function 0-3=-3.

As x gets larger and larger (towards ∞), the value of y, 2ˣ, continues to grow as well. Since it continues to grow exponentially, we say the value approaches ∞.

Answer 2

For very high x-values, f(x) moves toward positive infinity.

For very low x-values, f(x) moves towards negative infinity.

Explanation:

Here, the given function,

`f(x) = 2x - 3`

Which is a polynomial function,

Since, the end behaviour of a polynomial depends upon the leading coefficient and degree of the polynomial,

If degree = odd and leading coefficient = positive,

Then end behaviour of the function f(x) is,

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

`f(x)\rightarrow +\infty\text{ as }x\rightarrow +\infty`

∵ Here, the degree is odd ( 1 ) and leading coefficient = 2 ( even )

Thus, the above end behaviour is also the end behaviour of the given function.