Question

What does adding two strictly increasing functions or multiplying a strictly increasing function by a positive constant or another strictly increasing function result in?

a) A constant function
b) A decreasing function
c) An increasing function
d) A quadratic function

Answer 1

Adding two strictly increasing functions or multiplying a strictly increasing function by a positive constant or another strictly increasing function always results in an increasing function.

Step-by-step explanation:

When you add two strictly increasing functions together, or when you multiply a strictly increasing function by a positive constant or another strictly increasing function, the result is also an increasing function. Here's why:

• Adding two increasing functions: If f(x) and g(x) are both increasing, then for any two values a and b such that a < b, f(a) < f(b) and g(a) < g(b). So, (f+g)(a) = f(a) + g(a) < f(b) + g(b) = (f+g)(b), implying that f+g is also increasing.
• Multiplying by a positive constant: Multiplying an increasing function by a positive constant retains the direction of the increase but changes the rate at which the function increases.
• Multiplying two increasing functions: If f(x) and g(x) are increasing, then for any a < b, f(a) < f(b) and g(a) < g(b), and thus f(a)g(a) < f(b)g(b), so the product is also increasing.

Therefore, the correct answer to the question is c. An increasing function.