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Math  /  Algebra

QuestionUse graphing technology to find the domain of the function f(x)=−(x+5)2−1f(x)=-(x+5)^{2}-1.

Studdy Solution

STEP 1

1. The function f(x)=−(x+5)2−1 f(x) = -(x+5)^2 - 1 is a quadratic function.
2. The domain of a quadratic function is typically all real numbers unless otherwise restricted.
3. Graphing technology can help visualize the function to confirm the domain.

STEP 2

1. Analyze the structure of the function.
2. Use graphing technology to visualize the function.
3. Determine the domain from the graph.

STEP 3

Analyze the structure of the function f(x)=−(x+5)2−1 f(x) = -(x+5)^2 - 1 .
The function is a quadratic function in the form of ax2+bx+c ax^2 + bx + c , where a=−1 a = -1 , b=0 b = 0 , and c=−1 c = -1 . The negative sign in front of the squared term indicates that the parabola opens downwards.

STEP 4

Use graphing technology to visualize the function.
Input the function f(x)=−(x+5)2−1 f(x) = -(x+5)^2 - 1 into a graphing calculator or software. Observe the shape and direction of the parabola.

STEP 5

Determine the domain from the graph.
Since the graph of the function is a parabola that opens downwards and extends infinitely in both the left and right directions, the domain is all real numbers.
The domain of the function is (−∞,∞) (-\infty, \infty) .
The domain of the function is (−∞,∞) \boxed{(-\infty, \infty)} .

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