fill in the blank with the appropriate axis (x - axis or y - axis).\n(a) the graph of ( y=-f(x) ) is…

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

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

Answer

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