Construct a polynomial function of least degree possible using the given information.
1 answer:
Answer:
f(x) = (-5/3)x³ +5x² +(5/3)x -5
Step-by-step explanation:
For root "a", the polynomial will have a factor (x -a). Given the three roots, the polynomial will be the product of the three factors ...
... p(x) = (x +1)(x -1)(x -3)
The value of p(2) is 3·1·(-1) = -3. In order to make f(2) = 5, we need to multiply p(x) by -5/3.
... f(x) = (-5/3)p(x)
... f(x) = (-5/3)(x +1)(x -1)(x -3)
Expanding gives
... f(x) = (-5/3)x³ +5x² +(5/3)x -5
You might be interested in
Answer:
all real numbers
Step-by-step explanation:
As the graph goes up, it keeps going up and to the right. There is nothing telling us it will stop moving to the right at a certain point. It goes up much faster than it goes right, but it keeps going right and up forever. That makes the domain reach positive infinity. The same happens on the left side. As it goes down to the left, it keeps going left forever to negative infinity. That makes the domain all real numbers from negative infinity to positive infinity.
Domain: all real numbers
