Which values are within the domain of the function? Check all that apply.

• The function g(x) is defined for all real numbers x.

• The maximum value of the range is 4.

• The maximum value of the domain is 3.

• The range of g(x) is {y| –1 < y ≤ 4}.

• The domain of g(x) is {x| –4 < x ≤ 3}.

Solution:

We will be using the graph of the  domain and the range of g(x) to prove this.

Let's see step by step 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.

Thus, The maximum value of the range is 4, and the range of g(x) is {y| –1 < y ≤ 4}.

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Which values are within the domain of the function? Check all that apply.

Summary:

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}.