Question

fill in the blank with the appropriate axis (x - axis or y - axis).
(a) the graph of ( y=-f(x) ) is obtained from the graph of ( y = f(x) ) by reflecting about the - select -
(b) the graph of ( y = f(-x) ) is obtained from the graph of ( y = f(x) ) by reflecting about the - select -

Explanation:

Step1: Analyze \(y = -f(x)\)

For a function \(y = f(x)\), when we change it to \(y=-f(x)\), for each \(x\) - value, the \(y\) - value is the negative of the original \(y\) - value. This means that if \((x,y)\) is a point on \(y = f(x)\), then \((x, - y)\) is a point on \(y=-f(x)\). Reflecting a point \((x,y)\) to \((x, - y)\) is a reflection about the \(x\) - axis.

Step2: Analyze \(y = f(-x)\)

For a function \(y = f(x)\), when we change it to \(y = f(-x)\), for each \(y\) - value, the \(x\) - value is the negative of the original \(x\) - value. That is, if \((x,y)\) is a point on \(y = f(x)\), then \((-x,y)\) is a point on \(y = f(-x)\). Reflecting a point \((x,y)\) to \((-x,y)\) is a reflection about the \(y\) - axis.

Answer:

(a) \(x\) - axis
(b) \(y\) - axis