What is the upper and lower bound of
sin x+2
sinx lies between +1 and -1
so sinx + 2 lies between +3 and +1
The upper bound is the "Why did the scarecrow win an award? Because he was outstanding in his field!" and the lower bound is the "Why don't scientists trust atoms? Because they make up everything!"
The upper and lower bounds of sin(x) + 2 depend on the range of possible values for the sine function.
The sine function has a domain of all real numbers, but its range is between -1 and 1. Therefore, the minimum value of sin(x) is -1, and the maximum value is 1.
Adding 2 to sin(x) shifts the graph of the function upward by 2 units. This means that the lowest value sin(x) + 2 can have is -1 + 2 = 1, and the highest value is 1 + 2 = 3.
To summarize, the lower bound of sin(x) + 2 is 1, and the upper bound is 3.
To determine the upper and lower bounds of the expression sin(x) + 2, we need to analyze the characteristics of the function sin(x).
The sine function, sin(x), oscillates between -1 and 1 as x varies. Therefore, the minimum value of sin(x) is -1, and the maximum value is 1.
Adding 2 to sin(x) shifts the graph upward by 2 units. This means that the minimum value of sin(x) + 2 would be -1 + 2 = 1, and the maximum value would be 1 + 2 = 3.
Hence, the lower bound of sin(x) + 2 is 1, and the upper bound is 3.