Adding two functions results in h(x) = 4x, while multiplying the same functions results in j(x) = -5×2 – 12x – 4. Which statements des

Question

Adding two functions results in h(x) = 4x, while multiplying the same functions results in j(x) = -5×2 – 12x – 4.
Which statements describe f(x) and g(x), the original functions? Select two options.
Both functions must have a constant rate of change.
Both functions must have a y-intercept of 0.
The rate of change of f(x) and g(x) must be opposites.
The y-intercepts of f(x) and g(x) must be opposites.

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2 months 2021-10-15T23:51:50+00:00 1 Answer 0 views 0

1. When we multiply two functions, the degree is the sum of the original degrees. So, since the degree of the product is 2, we have two cases:

• One of the function has already degree 2, and the other is constant (degree 0)
• Both functions are linear.

The first case is actually impossible, because otherwise the sum would have degree 2 as well. So, we know that both and are linear. In other words, we have

for some

We know that the sum is

we deduce that

So, we know that:

• Both functions must be quadratic. FALSE, otherwise the product would have degree 4;
• Both functions must have a constant rate of change. TRUE, linear functions have a constant rate of change;
• Both functions must have a y-intercept of 0. FALSE, it is only required that the sum of the y-intercepts is 0, they don’t have to be both zero;
• The rate of change of f(x) and g(x) must be opposites. FALSE, their sum must be 4;
• The y-intercepts of f(x) and g(x) must be opposites. TRUE, their sum must be zero.