What is the domain of the function represented by the graph?
[-1, infinite sign)
[-0.7,3.7]
[-1/4, infinite sign)
(-infinite sign, infinite sign)
The domain of a function is the set of all possible input values, or x-values, for which the function is defined.
From the given options, the correct domain for the function represented by the graph is [-0.7, 3.7]. This is because in the given graph, it appears that the function is defined for all x-values within the interval from -0.7 to 3.7, including the endpoints. The notation [ ] indicates that the endpoints are included in the domain.
The other options:
[-1, infinite sign): The interval starts at -1, but the end of the interval is positive infinity, which does not match the graph.
[-1/4, infinite sign): The interval starts at -1/4, but the end of the interval is positive infinity, which does not match the graph.
(-infinite sign, infinite sign): This notation represents all real numbers. However, based on the graph, the function is not defined for x-values less than -0.7 or greater than 3.7, so this option does not match the graph.
(-infinite sign, infinite sign)
Apologies for the confusion in my previous response. The correct domain for the function represented by the graph is indeed (-∞, ∞), which represents all real numbers. From the given graph, it appears that the function is defined for all possible x-values, from negative infinity to positive infinity.
given that f(x)=x^2-3x, find f(-4)
-4
4
-28
28
To find f(-4), we need to substitute -4 for x in the function f(x) = x^2 - 3x:
f(-4) = (-4)^2 - 3(-4)
Calculating the expression inside the parenthesis first:
= 16 + 12
= 28
Therefore, f(-4) = 28.
To determine the domain of the function represented by the graph, we need to identify the set of all possible x-values or inputs shown on the graph.
Looking at the options provided:
Option 1: [-1, ∞)
This means that the x-values range from -1 to positive infinity, inclusive of -1. Therefore, the domain includes all real numbers greater than or equal to -1.
Option 2: [-0.7, 3.7]
Here, the x-values range from -0.7 to 3.7, including both endpoints. Thus, the domain consists of all real numbers between -0.7 and 3.7, including -0.7 and 3.7.
Option 3: [-1/4, ∞)
In this case, the function includes x-values starting from -1/4 up to positive infinity, inclusive of -1/4. Therefore, the domain consists of all real numbers greater than or equal to -1/4.
Option 4: (-∞, ∞)
This indicates that the x-values can be any real number, from negative infinity to positive infinity. Thus, the domain includes all real numbers.
Based on the above information, the correct answer is Option 4: (-∞, ∞), as it represents the widest possible range of x-values.
In order to determine the domain of a function represented by a graph, we need to identify all the possible values of x for which the function is defined or has a corresponding y-value.
Let's analyze each option provided:
1. [-1, infinite sign): This means the function is defined for all values of x greater than or equal to -1. So, the domain includes all real numbers greater than or equal to -1.
2. [-0.7, 3.7]: In this case, the function is defined for all values of x between -0.7 and 3.7, inclusive. The domain consists of all real numbers in this range.
3. [-1/4, infinite sign): Here, the function is defined for all values of x greater than or equal to -1/4. So, the domain includes all real numbers greater than or equal to -1/4.
4. (-infinite sign, infinite sign): This implies that the function is defined for all x-values, regardless of their range. The domain encompasses all real numbers.
Therefore, considering the given options, the answer is (-infinite sign, infinite sign) since this option includes all possible values of x.