Question

Choose all of the statements that are correct.

If f(2) = 5, then the function f passes through the point (5, 2).
If f(x) = 7, then the equation y = 7 is true.
If f(4) = y, then the equation y = 4 is true.
If y = f(x), then the function f passes through the point (x, f(x)).

Answer 1

The correct statements are that if f(x) = 7 then y = 7 is true and if y = f(x) then the function f passes through the point (x, f(x)). The statement that if f(2) = 5, then f passes through (5, 2) is incorrect, as it passes through (2, 5). Again, the statement that if f(4) = y, then y = 4 is true, is incorrect because it only says that y is the value of the function at x=4.

Step-by-step explanation:

From the given options, the correct statements associated with the function f(x) are determined by understanding basic function notation and graph interpretation.

• If f(2) = 5, then the function f does not pass through the point (5, 2). Instead, it passes through the point (2, 5).
• If f(x) = 7, then the equation y = 7 is true for all values of x, representing a horizontal line on the graph.
• If f(4) = y, then the equation y = 4 is not necessarily true; it only means that at x=4, the function has a value y.
• If y = f(x), then the function f indeed passes through the point (x, f(x)).