ch of these functions grows as x gets larger and larger. Which function eventually exceeds others? f(x)=2x^2-5 g(x)=6x h(x)=2^x+1

To determine which function grows as x gets larger and larger, we need to analyze the behavior of each function.<br /><br />1. $f(x)=2x^{2}-5$: This is a quadratic function. As x increases, the value of $f(x)$ will also increase, but at a decreasing rate.<br /><br />2. $g(x)=6x$: This is a linear function. As x increases, the value of $g(x)$ will also increase, but at a constant rate.<br /><br />3. $h(x)=2^{x}+1$: This is an exponential function. As x increases, the value of $h(x)$ will also increase, but at an increasing rate.<br /><br />Comparing the three functions, we can see that $h(x)=2^{x}+1$ will eventually exceed the other two functions as x gets larger and larger. This is because exponential functions grow faster than both quadratic and linear functions.<br /><br />Therefore, the function that eventually exceeds the others is $h(x)=2^{x}+1$.