the function f(x)=(x - 4)(x - 2) is shown. what is the range of the function? all real numbers less than or…

Explanation:

Step1: Expand the function

$f(x)=(x - 4)(x - 2)=x^{2}-2x-4x + 8=x^{2}-6x + 8$.

Step2: Find the vertex of the parabola

For a quadratic function $y=ax^{2}+bx + c$ ($a\neq0$), the $x$-coordinate of the vertex is $x=-\frac{b}{2a}$. Here $a = 1$, $b=-6$, so $x=-\frac{-6}{2\times1}=3$. Substitute $x = 3$ into $y=x^{2}-6x + 8$, we get $y=3^{2}-6\times3 + 8=9-18 + 8=-1$. Since $a = 1>0$, the parabola opens upward.

Answer:

all real numbers greater than or equal to -1