Answer:
The domain is all real numbers. The range is {y|y ≤ 16}
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}-2x+15[/tex]
This is the equation of a vertical parabola open downward
The vertex is a maximum
Find the vertex of the quadratic equation
[tex]f(x)-15=-x^{2}-2x[/tex]
[tex]f(x)-15=-(x^{2}+2x)[/tex]
[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]
[tex]f(x)-15-1=-(x^{2}+2x+1)[/tex]
[tex]f(x)-16=-(x^{2}+2x+1)[/tex]
[tex]f(x)-16=-(x+1)^{2}[/tex]
[tex]f(x)=-(x+1)^{2}+16[/tex] -----> 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
Answer:
The Answer Is B
Step-by-step explanation:
domain is all real numbers. The range is {y|y ≤ 16}.
