Question

Transformations??? I don't understand

State the various transformations applied to the base function f(x)=|x| to obtain a graph of the functiong(x) = |x + 1| - 2.

Answer 1

(a.)Horizontal shift of 1 unit to the left and a vertical shift upward of 2 units.
(b.)Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.
(c.)Horizontal shift of 1 unit to the right and a vertical shift downward of 2 units.
(d.)Horizontal shift of 1 unit to the right and a vertical shift upward of 2 units.

Answer 2

SHIFTS:


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~f(x)=\left| x \color{blue}{ -~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm{c} }\) units to the right.


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~f(x)=\left| x \color{blue}{ +~\rm{c} }\right| }\)
\(\large\color{blue}{ ~\rm{c} }\) units to the left.


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~f(x)=\left| x \right| \color{blue}{ +~\rm{c} }}\)
\(\large\color{blue}{ ~\rm{c} }\) units to up.


\(\large\color{black}{ f(x)=\left| x \right| ~~~~~\bf{\rightarrow}~~~~~f(x)=\left| x \right| \color{blue}{ -~\rm{c} }}\)
\(\large\color{blue}{ ~\rm{c} }\) units to down.

Answer 3

your function is supposed to be,
\(\large\color{black}{ f(x)=\left| x +1\right|+2 }\) is that correct?

Answer 4

or g(x)... f(x), g(x), h(x) ... makes no difference here.

Answer 5

it's supposed to be f(x) = |x + 1| - 2, not add 2

I messed up something else though, forgot to include the base function in original question, changing that now

Answer 6

\(\large\color{black}{ f(x)=\left| x +1\right|-2 }\)

Answer 7

sure...

Answer 8

just added the base function to original question, and changed the equals to subtract 2

Answer 9

sure:)

Answer 10

Do you understand tyhe rules I posted?

Answer 11

no

Answer 12

wait hang on they're starting to make sense

Answer 13

so the units will move to the left?

Answer 14

how many units to the left? which one is the shift to the left, the +1 on the inside, or the -2 on the outside?

Answer 15

1 unit to the left, the shift to the left is the +1 on the outside

Answer 16

so far my answer choices are either a or b?

Answer 17

yes that is correct. the +1, moves the f(x) 1 unit left.

Answer 18

Now, the "-2" part on the outside, is a shift where, and by how many units?

Answer 19

it's a downward shift because subtracting downward on a coordinate grid? and 2 units

Answer 20

yes. you are going 2 units down.

Answer 21

So my answer is B, Horizontal shift of 1 unit to the left and a vertical shift downward of 2 units.?

Answer 22

So g(x), the new function, is 1 units to the left and 2 units down, from the (initial) f(x).


yes, B....

Answer 23

thank you!!

Answer 24

I would write these rules somewhere on a paper so that you rememeber them. Because you will need them ....

Answer 25

i will

Answer 26

not only in algebra, but even on in calc1:) .... you welcome!