Answer :
Let's address each question step-by-step.
Question 13: Use the vertical line test to determine if the relation is a function.
The vertical line test is a method used to determine if a relation is a function. According to this test, if a vertical line can be drawn at any point on the graph of the relation and it intersects the graph at more than one point, then the relation is not a function. Conversely, if every vertical line intersects the graph at no more than one point, then the relation is a function.
Based on the answer given, the result is `yes`. Thus, we conclude that the relation is a function.
Answer: yes
Question 14: Which of the following is the domain for the function [tex]\( h(x)=3x^2 \)[/tex]?
The domain of a function is the set of all possible input values (x-values) that the function can accept.
For the function [tex]\( h(x) = 3x^2 \)[/tex], we need to determine all the x-values that we can input into the function. Since squaring a real number always yields a real result, there is no restriction on the values that [tex]\( x \)[/tex] can take. Therefore, [tex]\( x \)[/tex] can be any real number.
Thus, the domain of the function [tex]\( h(x) \)[/tex] is all real numbers, which is represented as [tex]\( (-\infty, \infty) \)[/tex].
Answer: [tex]\((- \infty, \infty)\)[/tex]
Question 13: Use the vertical line test to determine if the relation is a function.
The vertical line test is a method used to determine if a relation is a function. According to this test, if a vertical line can be drawn at any point on the graph of the relation and it intersects the graph at more than one point, then the relation is not a function. Conversely, if every vertical line intersects the graph at no more than one point, then the relation is a function.
Based on the answer given, the result is `yes`. Thus, we conclude that the relation is a function.
Answer: yes
Question 14: Which of the following is the domain for the function [tex]\( h(x)=3x^2 \)[/tex]?
The domain of a function is the set of all possible input values (x-values) that the function can accept.
For the function [tex]\( h(x) = 3x^2 \)[/tex], we need to determine all the x-values that we can input into the function. Since squaring a real number always yields a real result, there is no restriction on the values that [tex]\( x \)[/tex] can take. Therefore, [tex]\( x \)[/tex] can be any real number.
Thus, the domain of the function [tex]\( h(x) \)[/tex] is all real numbers, which is represented as [tex]\( (-\infty, \infty) \)[/tex].
Answer: [tex]\((- \infty, \infty)\)[/tex]
