Question

Describe the change to the parent function. I am not good at this and I don't really know how to describe each parent function.

1. y = -3sqrt x
2. y = 2/5sqrt x
3. y = sqrt -x + 3
4. y = sqrt x - 2
5. y = sqrt x + 2
6. y = sqrt x - 4
7. y = 2 sqrt -x + 1
8. y = - sqrt x - 5
9. y = 4 sqrt x + 3 -1
10. y = -1/3 sqrt x -1 + 3

Answer 1

hmm doyou have a parent function to start with?

Answer 2

the parent function is obvious: y = sqrt x

Answer 3

ok

Answer 4

so let's use that

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

\begin{array}{llll}

\begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array}
\qquad
\begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array}

\begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array}
\\

% template start
\qquad \downarrow\qquad\qquad\quad\ \downarrow\\
y = {\color{purple}{ A}} \sqrt{x+ {\color{red}{ C}}} + {\color{green}{ D}}\\
%template end
\qquad\qquad \quad \uparrow \\

\qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array}

\begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array}
\end{array}
}\)

see the shifts and expansions or shrinking?

Answer 5

a negative leading "A" value, means, the function is flipped upside down

Answer 6

don't forget B

Answer 7

hmmm I do have a "B", in a more general template
it's just no needed in this case

Answer 8

so let's see the 1st 3
\(\bf y={\color{purple}{ -3}}\sqrt{x}\qquad y={\color{purple}{ \cfrac{2}{3}}}\sqrt{x}\qquad \sqrt{-x{\color{red}{ +3}}}\)

actually the 3rd one, uses B

so lemme post that for that one then

Answer 9

\(\bf y={\color{purple}{ -3}}\sqrt{x}\qquad y={\color{purple}{ \cfrac{2}{3}}}\sqrt{x}\qquad \sqrt{{\color{blue}{ -1}}x{\color{red}{ +3}}}\)

and check the template
\(\large {
\textit{function transformations}
\\ \quad \\

\begin{array}{llll}

\begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\cdot {\color{blue}{ B}}\end{array}
\qquad
\begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array}

\begin{array}{llll}{\color{green}{ D}} > 0& Upwards
\\ \quad \\
{\color{green}{ D}} < 0 & Downwards\end{array}
\\

\qquad \downarrow\qquad\qquad\quad\ \downarrow\\
% template start
y = {\color{purple}{ A}} ( {\color{blue}{ B}}x + {\color{red}{ C}} ) + {\color{green}{ D}}\\
% template ends
\qquad\qquad\quad\ \uparrow \\

\qquad\begin{array}{llll} horizontal\\ shift\\ by \ \frac{{\color{red}{ C}}}{{\color{blue}{ B}}}\end{array}

\begin{array}{llll}\frac{{\color{red}{ C}}}{{\color{blue}{ B}}} > 0 & to\ the\ left
\\ \quad \\
\frac{{\color{red}{ C}}}{{\color{blue}{ B}}} < 0& to\ the\ right\end{array}
\end{array}
}\)

Answer 10

anyhow,, need to dash... but you can see
the 1st one
is flipped upside down, and shrinks by a factor of 3
2nd one
expands by a factor of 2/3

the bigger the number, it shrinks the graph, the smaller, it expands it

the 3rd one
has a horizontal shift of 3/-1 or -3
A* B means 1 * -1 => -1, so it's also flipped upside down

Answer 11

@satellite73 shouldn't #1 be: refected over x-axis and expansion by a factor of 3