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GB-35-07-001 · Graph reflection

The graph y = f(x) passes through (7,−7)(7,-7).

(a) Find the corresponding point on y = −f(x).

(b) Find the corresponding point on y = f(−x).

Part (a) Graph Transformations: Reflections Booklet p. 87
Method
Special Cases: y = −f(x) ⇒ reflection in x-axis (x, −y); y = f(−x) ⇒ reflection in y-axis (−x, y)
Worked Example (GB-35-07-001 · Part (a))
Find the corresponding point on y = −f(x).
1)
The minus sign outside f reflects in the x-axis: keep x, negate y.
2)
(7,−7)↦(7,7)(7,-7)\mapsto(7,7)
Ans = (7,7)(7,7)
Part (b) Graph Transformations: Reflections Booklet p. 87
Method
Special Cases: y = −f(x) ⇒ reflection in x-axis (x, −y); y = f(−x) ⇒ reflection in y-axis (−x, y)
Worked Example (GB-35-07-001 · Part (b))
Find the corresponding point on y = f(−x).
1)
The minus sign inside f reflects in the y-axis: negate x, keep y.
2)
(7,−7)↦(−7,−7)(7,-7)\mapsto(-7,-7)
Ans = (−7,−7)(-7,-7)