the function $f(x) = (x - 4)(x - 2)$ is shown.\nwhat is the range of the function?\nall real numbers less…

the function $f(x) = (x - 4)(x - 2)$ is shown.\nwhat is the range of the function?\nall real numbers less than or equal to 3\nall real numbers less than or equal to -1\nall real numbers greater than or equal to 3\nall real numbers greater than or equal to -1

the function $f(x) = (x - 4)(x - 2)$ is shown.\nwhat is the range of the function?\nall real numbers less than or equal to 3\nall real numbers less than or equal to -1\nall real numbers greater than or equal to 3\nall real numbers greater than or equal to -1

Answer

Explanation:

Step1: Expand the function

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

Step2: Find vertex x-coordinate

$x=-\frac{b}{2a}=-\frac{-6}{2(1)}=3$

Step3: Calculate vertex y-value

$f(3)=(3)^2-6(3)+8=9-18+8=-1$

Step4: Determine range direction

Since $a=1>0$, parabola opens upward, so the vertex is the minimum point.

Answer:

all real numbers greater than or equal to -1