michael2224
michael2224 michael2224
  • 23-06-2019
  • Mathematics
contestada

Which function has a range of {yly < 5}?
f(x) = (x - 4)^2 +5
f(x) = -(x-4)^2 + 5
f(x) = (x - 5)^2 + 4
f(x) = -(x – 5)^2 + 4​

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Prove Prove
  • 23-06-2019

Answer:

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

Step-by-step explanation:

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

Proving that [tex]f(x) = -(x-4)^2 + 5 \le 5[/tex] for all x:

[tex]x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.[/tex]

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