Question

which of the following accurately depicts the transformation of y=x^2 to the function below?

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

a. shift up 1 unit, stretch horizontally by a factor of 5, then shift 2 units
b. shift right 2 units, stretch vertically by a factor of 5, then shift up 1 unit
c. shift 5 units right, stretch vertically by factor of 2, shift up 1
d. shift right 2 units, shrink vertically to 1/5 of the original height, shift up 1

Answer 1

@RhondaSommer

Answer 2

\(\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 \\ \quad \\
\bf y={\color{purple}{ 5}}(x{\color{red}{ -2}})^2{\color{green}{ +1}}\)

any ideas?

Answer 3

is it C?

Answer 4

what makes you think is C?

Answer 5

no wait is it A because it shift horizontally and shifts up not down?

Answer 6

and does it shift left because 2 is negative? i think it's A

Answer 7

hmmmm notice the template, what happens when C/B is negative

Answer 8

ohh it shifts to the right

Answer 9

notice, you have x -2
or 1x-2
meaning B = 1, C= -2

Answer 10

yeap
expands by a factor of 5
shift horizontally to the "right" by 2 units
and goes up by 1

Answer 11

so it's D

Answer 12

mmm

actually a factor of 5, shrinks

anyhow

shrinks it by a factor of 5
shift horizontally to the "right" by 2 units
and goes up by 1

Answer 13

but check your choices more closely

Answer 14

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoiNSh4LTIpXjIrMSIsImNvbG9yIjoiI0RCMEQwRCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi01LjI2IiwiNy43NCIsIi0xLjUyIiwiNi40OCJdfV0- <---

Answer 15

the only one that shrinks is D??

Answer 16

hmmmm hmmm
I think.... yes.. you're correct.... it'd be D then

Answer 17

thank you!

Answer 18

yw