Question

let f(x) = 8^x and g(x) = 8(^x+5) + 1

which transformations are need to transform the graph of f(x) to the graph g(x)?

Answer 1

answers

Answer 2

\(\bf \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}
\\ \quad \\
-----------------------------\\
g(x)=8^{x+{\color{red}{ 5}}}+{\color{green}{ 1}}\)


you tell us

Answer 3

\(\large \bf g(x)=8^{{\color{blue}{ 1}} x+{\color{red}{ 5}}}+{\color{green}{ 1}}\) just clarifying a bit more, in case needed

Answer 4

Just what @jdoe0001 has written,,,,
What do you think, @uscrnamc?

How many steps in the horizontal direction \(\color{red}x\) and how many in the vertical direction \(\color{red}y\)?

Answer 5

the only one i really know that i did by myself is it went up 5 units

Answer 6

Just what @jdoe0001 has written,,,,

What do you think, @uscrnamc?
How many steps in the horizontal direction \(\color{red}x\) and how many in the vertical direction \(\color{red}y\)?

Answer 7

the 5 is "grouped" with the "x", thus is a horizontal shift, doesn't "go up by 5 units"
going up means, a vertical shift