The function f(x) = –x2 – 4x + 5 is shown on the graph. Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

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Today at 7:24 PM
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The function f(x) = –x2 – 4x + 5 is shown on the graph. Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.

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calculista calculista · Answer 1 · 2025-04-01T19:30:16-04:00

calculista calculista

Today at 7:30 PM

we have

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

using a graph tool

see the attached figure

the domain of the function is all real numbers------> the interval is (-∞,∞)

the range of the function is --------------------------------> the interval (-∞,9]

therefore

the answer is

The range of the function is all real numbers less than or equal to [tex] 9 [/tex]

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2025-04-01T19:29:58-04:00

The domain of the function is the all possible input values for the function and range is the all values of outputs for the function.

The domain of the function is all real numbers from [tex](-\infty, \infty)[/tex]

The range of the function is in the interval of [tex](-\infty, 9)[/tex]

What is domain and range of the function?

The domain of the function is the all possible input values for the function and range is the all values of outputs for the function.

Given information-

The function given in the problem is,

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

Rewrite the equation as,

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

Add and subtract 4 from the equation,

[tex]f(x) = -(x +4x) + 5+4-4\\f(x) = -(x +4x+4) + 9\\f(x) = -(x +2) ^2+ 9\\[/tex]

Compare it with the vertex form, we get,

[tex]a=-1\\h=2\\k=9[/tex]

As the value of a is negative, thus the parabola opens down as shown in attached image. The vertex are (2,9) and extent to infinity.

Thus,

The domain of the function is all real numbers from [tex](-\infty, \infty)[/tex]

The range of the function is in the interval of [tex](-\infty, 9)[/tex]

Learn more about the range and domain of the function here;

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