which function has a range of {y|y ≤ 5}?\n○ f(x)=(x - 4)^2+5\n○ f(x)=-(x - 4)^2+5\n○ f(x)=(x - 5)^2+4\n○…

Explanation:

Step1: Recall vertex - form of a quadratic function

The vertex - form of a quadratic function is $f(x)=a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola. If $a>0$, the parabola opens upward and the range is $y\geq k$. If $a < 0$, the parabola opens downward and the range is $y\leq k$.

Step2: Analyze each option

Option 1: $f(x)=(x - 4)^2+5$

Here $a = 1>0$, the parabola opens upward and the range is $y\geq5$.

Option 2: $f(x)=-(x - 4)^2+5$

Here $a=-1<0$, the vertex is $(4,5)$. Since the parabola opens downward, the range is $y\leq5$.

Option 3: $f(x)=(x - 5)^2+4$

Here $a = 1>0$, the parabola opens upward and the range is $y\geq4$.

Option 4: $f(x)=-(x - 5)^2+4$

Here $a=-1<0$, the vertex is $(5,4)$ and the range is $y\leq4$.

Answer:

$f(x)=-(x - 4)^2+5$