Which function would yield the highest value if x is increased continuously?

Which function would yield the highest value if x is increased continuously?

• A. 2x + 5
• B. x² + 3x
• C. 5x - 4
• D. 3x + 1

Answer: (B)

To determine which function yields the highest value as x increases, it's essential to analyze the growth rates of each option. The function x² + 3x represents a quadratic function. In general, quadratic functions will grow faster than linear functions as x becomes large due to the squared term. In this case, the x² component increases significantly faster than the linear components of the other functions. The function 2x + 5 is a linear function with a slope of 2, meaning it increases at a constant rate as x increases. Similarly, 5x - 4 and 3x + 1 are also linear functions, with slopes of 5 and 3 respectively. While these functions will continue to grow as x increases, their rates of increase are limited compared to the quadratic growth of x² + 3x. Therefore, as x continues to increase, the x² term in the quadratic function will dominate the growth, leading to the conclusion that x² + 3x yields the highest values in comparison to the other functions listed.

To determine which function yields the highest value as x increases, it's essential to analyze the growth rates of each option.

The function x² + 3x represents a quadratic function. In general, quadratic functions will grow faster than linear functions as x becomes large due to the squared term. In this case, the x² component increases significantly faster than the linear components of the other functions.

The function 2x + 5 is a linear function with a slope of 2, meaning it increases at a constant rate as x increases. Similarly, 5x - 4 and 3x + 1 are also linear functions, with slopes of 5 and 3 respectively. While these functions will continue to grow as x increases, their rates of increase are limited compared to the quadratic growth of x² + 3x.

Therefore, as x continues to increase, the x² term in the quadratic function will dominate the growth, leading to the conclusion that x² + 3x yields the highest values in comparison to the other functions listed.