Determine whether each statement is true or false. Explain your reasoning.
The equation y = x3 describes y as a function of x.
Answer
True. For any value of x there is only one value of y.
Example 2
Determine whether each statement is true or false. Explain your reasoning.
The equation y = x3 describes x as a function of y.
Answer
True. For any value of y there is only one value of x, since each real number has only one cube root.
Example 3
Determine whether each statement is true or false. Explain your reasoning.
The equation z = 8x describes x as a function of z.
Answer
True. For any value of z we have , there is only one possible value of x.
Example 4
Determine whether each statement is true or false. Explain your reasoning.
The equation z = y4 describes z as a function ofy.
Answer
True. For any value of y there is only one possible value of z.
Example 5
Determine whether each statement is true or false. Explain your reasoning.
The equation z = y4 describes y as a function of z.
Answer
False. For any value of z there are two possible values of y. For example, if z = 16 then y can be ± 2. Watch out for these sneaky functions where the independent variable is raised to by even-valued exponent. They have two roots, the positive number and their evil negative twin.
, there is only one possible value of x.