yes
No, the sum of two power functions is not always a power function. For example, if we take ( f(x) = x^2 ) and ( g(x) = x^3 ), their sum ( f(x) + g(x) = x^2 + x^3 ) is not a power function, as it cannot be expressed in the form ( x^k ) for a single exponent ( k ). In general, the sum of two power functions with different exponents yields a polynomial rather than a single power function.
Well, it sounds like a plausible statement, and maybe it would be true . But we haveno idea what the graph of two functions is.Perhaps you could graph the sum of two functions, or the difference of two functions,or their product, or their quotient. We believe that if the original two functions areboth continuous, then their sum and difference would also be continuous, but theirproduct and their quotient might not necessarily be continuous. However, we stilldon't know what the "graph of two functions" is.
The sum of two odd numbers is always even.
No, the sum of two vectors cannot be a scalar.
Yes the sum of two integers will always be an integer.
Yes. You would have to multiply to change it.
Well, it sounds like a plausible statement, and maybe it would be true . But we haveno idea what the graph of two functions is.Perhaps you could graph the sum of two functions, or the difference of two functions,or their product, or their quotient. We believe that if the original two functions areboth continuous, then their sum and difference would also be continuous, but theirproduct and their quotient might not necessarily be continuous. However, we stilldon't know what the "graph of two functions" is.
The sum of two odd numbers is always even.
No, the sum of two vectors cannot be a scalar.
No, the sum of two consecutive numbers is always an odd number, and is not divisible by two.
Yes the sum of two integers will always be an integer.
Such a sum is always rational.
No. While the sum of two qudratics cannot have a power greater than two, it could have a power of 2, 1 or 0. x2 + 1 is one quadratic (2-x)(2+x) is another quadratic. Their sum is 1, a constant (power = 0).
Yes, by definition, the sum of two integers is always an integer. Likewise, the product and difference of two integers is always an integer.
The sum of two even numbers is always an even number.
The sum of two positive numbers is always a positive number.
The sum of two odd numbers is always an even number