QuestionQuestion 7 of 18 This quiz: 18 point(s) possible This question: 1 point(s) possil
Determine the domain and range of the following function. The function's graph is shown to the right. $y=x^{2}-4$
What is the domain? The domain is $\square$ (Type your answer in interval notation.) What is the range? The range is $\square$ . (Type your answer in interval notation.)

Studdy Solution

STEP 1

1. The function given is $y = x^2 - 4$ .
2. The graph of the function is a parabola opening upwards.
3. We need to determine the domain and range of the function.

STEP 2

1. Determine the domain of the function.
2. Determine the range of the function.

STEP 3

The domain of a quadratic function $y = x^2 - 4$ is determined by the values of $x$ for which the function is defined. Since there are no restrictions on $x$ (such as division by zero or square roots of negative numbers), the domain is all real numbers.
The domain in interval notation is: $(-\infty, \infty)$

STEP 4

The range of the function $y = x^2 - 4$ is determined by the values that $y$ can take. The vertex of the parabola, which is the minimum point, occurs at $x = 0$ . Substituting $x = 0$ into the function gives $y = 0^2 - 4 = -4$ .
Since the parabola opens upwards, the range of $y$ starts at $-4$ and goes to infinity.
The range in interval notation is: $[-4, \infty)$
The domain is: $(-\infty, \infty)$
The range is: $[-4, \infty)$

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