Which values are within the domain of the function? Check all that apply.
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The function g(x) is defined for all real numbers x.
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The maximum value of the range is 4.
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The maximum value of the domain is 3.
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The range of g(x) is {y| –1 < y ≤ 4}.
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The domain of g(x) is {x| –4 < x ≤ 3}.
We will be using the graph of the domain and the range of g(x) to prove this.
Answer: Values within the domain of the function are (b) The maximum value of the range is 4, (d) the range of g(x) is {y| –1 < y ≤ 4}.
Let's see step by step explanation.
Explanation:
First, it is important to understand that the domain is all possible x values, and the range is all possible y values.
As per the graph,
The domain of g(x) is -4 ≤ x ≤ -1 & 0 ≤ x < 3.
The range of g(x) is -1 < y ≤ 4.
Option 1: We know the graph is not defined for all values of x because the domain only refers to certain x values.
Option 2: This is true because the range extends from -1 to 4, so 4 is the largest possible value.
Option 3: It is incorrect because our domain extends from -4 to 3; 3 is noninclusive.
Option 4: This is correct because the range extends from -1 to 4.
Option 5: The last choice is incorrect because no x values between -1 and 0 are defined.