Question

What is the end behavior of function h?

hx=2(x-3)²
As xapproaches negative infinity, hx approaches ______
As x approaches positive infinity, hx approaches ____

Answer 1

The end behavior of the function h(x) = 2(x - 3)^2 is such that as x approaches negative infinity, h(x) approaches positive infinity, and as x approaches positive infinity, h(x) also approaches positive infinity.

Step-by-step explanation:

The end behavior of the function h(x) = 2(x - 3)2 differs as x approaches negative infinity and positive infinity. Since this is a quadratic function with a positive leading coefficient, the parabola opens upwards. Therefore, as x approaches negative infinity, h(x) approaches positive infinity because the function will rise without bound in the negative x-direction. Similarly, as x approaches positive infinity, h(x) also approaches positive infinity, as the function continues to rise without bound in the positive x-direction.