The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is y. The domain is all real nu…

Question

The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is y < 16. The domain is all real numbers. The range is y. The domain is –5 < x < 3. The range is y. The domain is –5 ≤ x ≤ 3. The range is y.

Answer 1

The Answer Is B

Explanation:

domain is all real numbers. The range is y.

Answer 2

The domain is all real numbers. The range is y

Explanation:

we have

`f(x)=-x^(2)-2x+15`

This is the equation of a vertical parabola open downward

The vertex is a maximum

Find the vertex of the quadratic equation

`f(x)-15=-x^(2)-2x`

`f(x)-15=-(x^(2)+2x)`

`f(x)-15-1=-(x^(2)+2x+1)`

`f(x)-15-1=-(x^(2)+2x+1)`

`f(x)-16=-(x^(2)+2x+1)`

`f(x)-16=-(x+1)^(2)`

`f(x)=-(x+1)^(2)+16` -----> equation in vertex form

The vertex is the point (-1,16)

therefore

The domain is the interval ----> (-∞,∞) All real numbers

The range is the interval ----> (-∞,16] All real numbers less than or equal to 16