Identify the maximum or minimum value and the domain and range of the graph of the function y = 2(x – 3)2 – 4.
(1 point)
Responses
minimum value: –4
domain: all real numbers
range: all real numbers greater than equal to–4
minimum value: –4 domain: all real numbers range: all real numbers Image with alt text: greater than equal to –4
maximum value: 4
domain: all real numbers
range: all real numbers A symbol less than or equal to4
maximum value: 4 domain: all real numbers range: all real numbers Image with alt text: A symbol less than or equal to 4
maximum value: –4
domain: all real numbers A symbol less than or equal to–4
range: all real numbers
maximum value: –4 domain: all real numbers Image with alt text: A symbol less than or equal to –4 range: all real numbers
minimum value: 4
domain: all real numbers greater than equal to4
range: all real numbers
The correct response is:
maximum value: 4
domain: all real numbers
range: all real numbers greater than or equal to -4
Are you sure
Apologies for the confusion. Let's analyze the given function:
y = 2(x - 3)^2 - 4
This is a quadratic function in the form y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, the vertex has coordinates (3, -4).
Since the coefficient of the squared term (2) is positive, the parabola opens upwards, indicating that the vertex represents the minimum value of the function.
So, the correct response is:
Minimum value: -4
Domain: all real numbers
Range: all real numbers greater than or equal to -4
maximum value: 4
domain: all real numbers
range: all real numbers greater than or equal to -4
The correct response would be:
minimum value: -4
domain: all real numbers
range: all real numbers greater than or equal to -4
To explain how to find the minimum value, domain, and range of the function y = 2(x – 3)² – 4:
1. Minimum value: The minimum value of a quadratic function can be found by looking at the coefficient of the squared term. In this case, the coefficient is 2, which is positive. This means that the parabola opens upwards and the minimum value occurs at the vertex of the parabola. In the given function, the vertex is at (3, -4), which gives us the minimum value of -4.
2. Domain: The domain of a function is the set of all possible x-values for which the function is defined. In this case, since there are no restrictions or limitations in the given function, the domain is all real numbers.
3. Range: The range of a function is the set of all possible y-values that the function can take on. In this case, since the coefficient of the squared term is positive, the parabola opens upwards and the y-values will continuously increase as x moves to the left or right without bound. Therefore, the range is all real numbers greater than or equal to -4.