Question

Which function has a range of {yly < 5}?

Answer 1

Answer:

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

Step-by-step explanation:

The function $f(x) = -(x-4)^2 + 5$ is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.

Proving that $f(x) = -(x-4)^2 + 5 \le 5$ for all x:

$x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.$