Question

How does the graph of each function compare to the graph of the parent function?

y=5(2)^(x+1) +3

Answer 1

hmm what's the parent function?

Answer 2

It doesnt say

Answer 3

this is all the information that is given

Answer 4

so..hmm have you covered "function transformations" yet?

Answer 5

yes

Answer 6

its really written like this \[5(2)^{x+1}+3\]

Answer 7

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

\begin{array}{rllll}
% left side templates

f(x)=&{\color{purple}{ A}}\mathbb{R}^{{\color{blue}{ B}}x+{\color{red}{ C}}}+{\color{green}{ D}}
\\ \quad \\
f(x)=&{\color{purple}{ 5}}(2)^{{\color{blue}{ 1}}x+{\color{red}{ 1}}}+{\color{green}{ 3}}
\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}\)

the parent would then be \(\Large f(x) = 5(2)^x\)

and this one, is just a "transformed version" of that one
meaning, is the same graph, but shifted up/down/left/right around

Answer 8

so. notice the template
B 1 one, no change from the original
but
C is +1, meaning, it shifts to the LEFT by 1 unit
and
D is +3, meaning, it goes up by 3 units

Answer 9

OMG this is very helpful, I appreciate this a lot. thank dude take a medal

Answer 10

yw

Answer 11

\(\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}\)


:)

also applies to trigonometric functions btw

Answer 12

hey does A stretch and 0.A shrinks?