Mathematics
kprichard2000
2016-04-12 10:38:06
Which function represents g(x), a reflection of f(x) = 4across the x-axis? g ( x ) = -4 (2) x g ( x ) = 4 (2) -x g ( x ) = -4 g ( x ) = 4
ANSWERS
Darlenedogcat
2016-04-12 12:32:55

[latex]f qquad qquad qquad qquad extit{function transformations} \ quad \\ % left side templates egin{array}{llll} f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \ quad \ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \ quad \ f(x)=&{{ A}}sqrt{{{ B}}x+{{ C}}}+{{ D}} \ quad \ f(x)=&{{ A}}(mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}} \ quad \ f(x)=&{{ A}} sinleft({{ B }}x+{{ C}} ight)+{{ D}} end{array}\\ --------------------\\[/latex] [latex]f ullet extit{ stretches or shrinks horizontally by } {{ A}}cdot {{ B}}\\ ullet extit{ flips it upside-down if }{{ A}} extit{ is negative}\ left. qquad ight. extit{reflection over the x-axis} \\ ullet extit{ flips it sideways if }{{ B}} extit{ is negative}\ left. qquad ight. extit{reflection over the y-axis} \\ ullet extit{ horizontal shift by }frac{{{ C}}}{{{ B}}}\[/latex] [latex]f left. qquad ight. if frac{{{ C}}}{{{ B}}} extit{ is negative, to the right}\\ left. qquad ight. if frac{{{ C}}}{{{ B}}} extit{ is positive, to the left}\\ ullet extit{ vertical shift by }{{ D}}\ left. qquad ight. if {{ D}} extit{ is negative, downwards}\\ left. qquad ight. if {{ D}} extit{ is positive, upwards}\\ ullet extit{ period of }frac{2pi }{{{ B}}}[/latex] now, if f(x) = 4 then a reflection over the x-axis is the same function with a negative A component, thus -4

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