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Which function has a range of vy s 5)?
of(x) = (x - 4)2 + 5
O (x) = -(x - 4)2 + 5
o f(x) = (x - 5)2 + 4
Of(x) = -(x - 5)2 + 4

Respuesta :

calculista

Answer:

see the explanation

Step-by-step explanation:

Verify the range of each quadratic function

case 1) we have

[tex]f(x)=(x-4)^2+5[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The function is written in vertex form

The vertex represent a minimum

The vertex is the point (4,5)

The range is the interval [5,∞)

[tex]y\geq 5[/tex]

case 2) we have

[tex]f(x)=-(x-4)^2+5[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The function is written in vertex form

The vertex represent a maximum

The vertex is the point (4,5)

The range is the interval (-∞,5]

[tex]y\leq 5[/tex]

case 3) we have

[tex]f(x)=(x-5)^2+4[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The function is written in vertex form

The vertex represent a minimum

The vertex is the point (5,4)

The range is the interval [4,∞)

[tex]y\geq 4[/tex]

case 4) we have

[tex]f(x)=-(x-5)^2+4[/tex]

This is a vertical parabola open downward (the leading coefficient is negative)

The function is written in vertex form

The vertex represent a maximum

The vertex is the point (5,4)

The range is the interval (-∞,4]

[tex]y\leq 4[/tex]

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