Question

Which function below has the end behavior as and as ?.

a) Quadratic function
b) Exponential function
c) Logarithmic function
d) Linear function

Answer 1

The function that has an end behavior as x approaches positive infinity the function grows without bound and as x approaches negative infinity the function decreases without bound is the exponential function (option d).

Step-by-step explanation:

The function that has an end behavior as x approaches positive infinity the function grows without bound and as x approaches negative infinity the function decreases without bound is the exponential function (option d).

An exponential function is represented by the equation y = a * b^x, where a and b are constants and b is greater than 1. As x approaches positive infinity, the function grows exponentially because each successive value of x increases the value of y by multiplying it by b. As x approaches negative infinity, the function decreases exponentially because each successive value of x decreases the value of y by dividing it by b.

For example, y = 2^x is an exponential function. As x approaches positive infinity, y grows without bound. And as x approaches negative infinity, y decreases without bound.