Select all the true statements about identities.
A) You may use proven identities to prove other identities.
B) An identity is true only for restricted values of the variables.
C) You can prove an identity by graphing the side to the left of the equal sign, graphing the side to the right of the equal sign, and looking to see whether the two graphs coincide.
D) An identity is true regardless of the values you substitute for the variables.
Anonymous
To determine which statements about identities are true, let's evaluate each statement individually:
A) You may use proven identities to prove other identities.
This statement is true. Identities are mathematical equations that hold true for all values of the variables. If you have already proven an identity, you can use it as a starting point to prove other identities.
B) An identity is true only for restricted values of the variables.
This statement is false. An identity is true regardless of the values you substitute for the variables. It holds true for all possible values of the variables.
C) You can prove an identity by graphing the side to the left of the equal sign, graphing the side to the right of the equal sign, and looking to see whether the two graphs coincide.
This statement is false. While graphing can be a useful tool to provide evidence or intuition behind an identity, it is not a formal or conclusive way to prove an identity. Proving identities usually involves algebraic manipulations and logical deductions.
D) An identity is true regardless of the values you substitute for the variables.
This statement is true. As mentioned earlier, an identity holds true for all possible values of the variables. It is a fundamental property of an identity.
Based on the analysis above, the true statements about identities are:
A) You may use proven identities to prove other identities.
D) An identity is true regardless of the values you substitute for the variables.