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