Question

Given the function f(x) = x^2 and k = –3, which of the following represents a vertical shift?

f(x) + k
kf(x)
f(x + k)
f(kx)

Answer 1

\(\qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\

\begin{array}{rllll}
% left side templates
f(x)=&{\color{purple}{ A}}({\color{blue}{ B}}x+{\color{red}{ C}})+{\color{green}{ D}}
\\ \quad \\
y=&{\color{purple}{ A}}({\color{blue}{ B}}x+{\color{red}{ C}})+{\color{green}{ D}}
\\ \quad \\
f(x)=&{\color{purple}{ A}}\sqrt{{\color{blue}{ B}}x+{\color{red}{ C}}}+{\color{green}{ D}}
\\ \quad \\
f(x)=&{\color{purple}{ A}}\mathbb{R}^{{\color{blue}{ B}}x+{\color{red}{ C}}}+{\color{green}{ D}}
\end{array}\qquad

\begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {\color{purple}{ A}}\cdot {\color{blue}{ B}}\\
\bullet \textit{ horizontal shift by }\frac{{\color{red}{ C}}}{{\color{blue}{ B}}}\\
\qquad if\ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}}\textit{ is negative, to the right}\\
\qquad if\ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}}\textit{ is positive, to the left}\\
\bullet \textit{ vertical shift by }{\color{green}{ D}}\\
\qquad if\ {\color{green}{ D}}\textit{ is negative, downwards}\\
\qquad if\ {\color{green}{ D}}\textit{ is positive, upwards}
\end{array}\)

which one would that be anyway?

Answer 2

notice when a vertical shift occurs, when D is either positive or negative
now, check your choices