The graph of an absolute value function opens up and has a vertex of (0, -3). The domain of the function is . The range of the function is
Domain, all real numbers, ( - ∞,∞ )
Range, all y ≥ - 3, [ - 3,∞ )
Well, the domain of an absolute value function is all real numbers, since you can take the absolute value of any input. As for the range, it's like a clown's juggling balls - it goes both up and down! The range of this absolute value function is all values greater than or equal to -3. So, the range can be represented as (-3, ∞). Happy juggling!
To determine the domain of the absolute value function, we need to identify the set of all possible input values (x-values) for the function. Since the graph opens up and the vertex is at (0, -3), the function includes all values of x. Therefore, the domain of the function is the set of all real numbers, which can be expressed as (-∞, ∞).
To determine the range of the absolute value function, we need to identify the set of all possible output values (y-values) for the function. Since the graph opens up, the minimum value of the function is the y-coordinate of the vertex, which is -3. As the absolute value function continues to increase, there is no maximum value. Therefore, the range of the function is (-3, ∞).
To determine the domain and range of an absolute value function, we need to understand how absolute value functions behave.
The general form of an absolute value function is f(x) = |x - h| + k, where (h, k) represents the vertex of the function.
In this case, we are given that the vertex is at (0, -3). Therefore, our function can be written as f(x) = |x - 0| -3 = |x| - 3.
The vertex of the absolute value function is the lowest point on the graph if it opens upward or the highest point if it opens downward. Since the given absolute value function opens upward, the vertex (0, -3) is the lowest point on the graph.
Now, let's determine the domain of the function. The domain of an absolute value function is the set of all possible x-values for which the function is defined. In other words, it is the set of all real numbers.
Therefore, the domain of the given function is (-∞, ∞).
Next, let's determine the range of the function. The range of an absolute value function is the set of all possible y-values or the output values.
Since the graph of this absolute value function opens upward, it is symmetric about the vertex. This means that there is no upper bound on the y-values, and the minimum y-value is the y-coordinate of the vertex, which is -3.
Therefore, the range of the given function is (-3, ∞).