Question

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

Answer 1

`\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\\\ % left side templates \begin{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}} sin\left({{ B }}x+{{ C}} \right)+{{ D}} \end{array}\\\\ --------------------\\\\`


`\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\`


`\bf \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}`

now, if f(x) = 4
then a reflection over the x-axis is the same function with a negative A component, thus -4

Answer 2

The function that represents g(x), a reflection of f(x) = 4 across the x-axis is:

`g(x)=-4`

Explanation:

We are given a parent function f(x) as:

`f(x)=4`

We know that any function f(x) when is reflecting across the x-axis then the transformed function i.e. g(x) is given by:

`g(x)=-f(x)`

Hence, here the transformed function g(x) that is obtained by transforming f(x) is given by:

`g(x)=-4`