Question

Are my answers correct?

Answer 1

1. If a function f(x) is shifted to the left one unit, what function represents the transformation?

my answer: f(x+1)

Answer 2

2.) Let g(x) be the reflection of f(x) = x² + 5 in the x-axis. What is a function rule for g(x)?

my answer: g(x)=x^2-5?

Answer 3

thank you for coming

Answer 4

hmmmm how did you get "f(x+1)" for the 1st one?

Answer 5

Is it not right?

Answer 6

hint: \(\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}} ( 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}\)

Answer 7

y = f(x) + n shifts f(x) n units upward.? then

Answer 8

well, we dunno if its "right"
so...how do "you" know is right anyway?

Answer 9

I got my answer from another guy on here so I am not sure....how it was solved....

Answer 10

But it is wrong?

Answer 11

is number two correct? I actually did that one myself.

Answer 12

well.... hmm we dunno
check the template -> \(\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}} ( 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}\)

what do you think?

notice when the "horizontal shift" occurs
if C<0, that is, negative, to the right
if C>0, that is, positive, to the left

Answer 13

I am 99% sure that one is correct. Also....so you are saying I got number two correct then

Answer 14

I am only trying to get confirmation here.

Answer 15

99%? well, you must have a reason for that, right? :)

Answer 16

well... .based on that template

yes, 1st one is correct

just notice how the template works :)
(x+1) will make C - +1, and thus will shift it horizontally to the left

Answer 17

mmk, thank you.

Answer 18

and number two is correct as well

Answer 19

hmmm one sec
lemme show a simple graph and its relfection
notice what changed

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjAsImVxIjoiLXheMiIsImNvbG9yIjoiI0U4MDkwOSJ9LHsidHlwZSI6MTAwMH1d

what do you think?

Answer 20

now lemme quickly do \(x^2+5\

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIrNSIsImNvbG9yIjoiIzFFMkRENCJ9LHsidHlwZSI6MCwiZXEiOiIteF4yLTUiLCJjb2xvciI6IiNFODA5MDkifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyItMjUuNTI3OTU0MTAxNTYyNDkiLCIyNC4wNjMxMTAzNTE1NjI0OSIsIi0xNS4xOTc3NTM5MDYyNDk5OTMiLCIxNS4zMTk4MjQyMTg3NDk5OTMiXX1d

what do you think changed?

Answer 21

yes...thank you

Answer 22

anyhow
tis quite obvious, to get a reflection over the x-axis
you simply need to multiply all terms by -1 :)
that is
f(x) has a reflection over x-axis at -1 * f(x) or -f(x)
in this case \(-x^2-5\)

Answer 23

yw