Question

The function f(x) = –0.3(x – 5)2 + 5 is graphed. What are some of its key features? Check all that apply. The axis of symmetry is x = 5. The domain is {x| x is a real number}. The function is increasing over (–∞, 5). The minimum is (5, 5). The range is {y| y ≥ 5}.

Answer 1

Test statement #1.
f(x) = -0.3(x - 5)² + 5 
This is the equation of a parabola with vertex at (5,5).
Therefore the function is symmetric about x=5.
The statement "The axis of symmetry is x=5" is TRUE.

Test statement #2.
f(x) is defined for all real values of x.
The statement "The domain is {x | x is a real nuber} is TRUE.

Test statement #3.
As x -> -∞, f(x) -> -∞.
f(5) = -0.3*(5-5)^2 + 5 = 5
Therefore f(x) is creasing over (-∞, 5) is TRUE.

Test statement #4.
As x -> +∞, f(x) -> -∞.
Therefore the curve is concave downward., and it has no minimum.
The statement "The minimum is (5,5)" is False.

Test statement #5.
The maximum value of f(x) occurs at the vertex because the curve is concave downward.
The statement "The range is {y | y≥5}" is False.

Answer:
The first three statements are True. The last two statements are False.

Answer 2

Answer:

1 , 2, 3

Step-by-step explanation: