the function f(x)=-x² - 2x + 15 is shown on the graph. what are the domain and range of the function? the…

Explanation:

Step1: Identify domain of quadratic function

For a quadratic function $f(x)=-x^{2}-2x + 15$, domain of all quadratic functions is all real numbers since we can substitute any real - valued $x$ into the function.

Step2: Find the vertex of the parabola

The $x$ - coordinate of the vertex of a parabola $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Here $a=-1$, $b = - 2$, so $x=-\frac{-2}{2\times(-1)}=-1$. Substitute $x = - 1$ into $y=-x^{2}-2x + 15$: $y=-(-1)^{2}-2\times(-1)+15=-1 + 2+15 = 16$. Since $a=-1<0$, the parabola opens downwards. So the maximum value of the function is $y = 16$, and the range is ${y|y\leq16}$.

Answer:

The domain is all real numbers. The range is ${y|y\leq16}$.