Answer:
the answer is 1,3,4
Step-by-step explanation:
Source: Dude trust me
The functions that have greater maximums are:
[tex]\mathbf{f(x) = -(x + 1)^2 - 2}[/tex] and [tex]\mathbf{f(x) = -|2x| +3}[/tex]
The function g(x) is given as:
[tex]\mathbf{g(x) = -(x + 3)^2 - 4}[/tex]
The above function is a quadratic function, and it is represented as:
[tex]\mathbf{g(x) = a(x - h)^2 + k}[/tex]
Where the maximum value of the function is represented as:
[tex]\mathbf{g(h) = k}[/tex]
The above means that, the maximum of [tex]\mathbf{g(x) = -(x + 3)^2 - 4}[/tex] is
[tex]\mathbf{g(3) = -4}[/tex]
The maximum is -4
Similarly, the maximum of [tex]\mathbf{f(x) = -(x + 1)^2 - 2}[/tex] is
[tex]\mathbf{f(1) = -2}[/tex]
The maximum is -2
-2 is greater than -1. So,
[tex]\mathbf{f(x) = -(x + 1)^2 - 2}[/tex] has a greater maximum
Options (b) and (c) are absolute functions, and they are represented as:
[tex]\mathbf{g(x) = a|x - h| + k}[/tex]
Where the maximum value of the function is represented as:
[tex]\mathbf{g(h) = k}[/tex]
The above means that, the maximum of [tex]\mathbf{f(x) = -|x + 4| - 5}[/tex] is
[tex]\mathbf{f(4) = -5}[/tex]
The maximum is -5
-5 is not greater than -1. So,
[tex]\mathbf{f(x) = -|x + 4| - 5}[/tex] does not have a greater maximum
Similarly, the maximum of [tex]\mathbf{f(x) = -|2x| +3}[/tex] is
[tex]\mathbf{f(0) = 3}[/tex]
The maximum is 3
3 is greater than -1.
So,
[tex]\mathbf{f(x) = -|2x| +3}[/tex] has a greater maximum
Hence, the functions that have greater maximums are:
[tex]\mathbf{f(x) = -(x + 1)^2 - 2}[/tex] and [tex]\mathbf{f(x) = -|2x| +3}[/tex]
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