Question

What is the equation of the absolute value function?

Answer 1

and the choices are

Answer 2

i tried to solve and i got B but it was wrong, the top one id the graph for the question

Answer 3

that -4 parts actually shift this function down, not up. so you are looking for one with +4

Answer 4

so then will it be D, that what i thought at first but the -x confused me, ive never seen that before

Answer 5

"What is the equation of the absolute value function?" <--- I see the choices... just not what to match them against

Answer 6

do you know the graph of |x| ?

Answer 7

the graph is in my next post

Answer 8

no but isn't it always positive because of the absolute value

Answer 9

yeap so... for y = |x| when say \(\bf x=\pm 25\quad y = 25\)
or \(\bf x=\pm 5\quad y=5\)

so yes, even when "x" is negative, "y" is always positive, so

Answer 10

keep in mind function transformations that is, let's see the template

y = A | Bx + C | + D

C = horizontal shift, C > 0, to the left, C < 0, to the right

D = vertical shift, D > 0, up, D < 0 down

A = expands or shrinks the graph

Answer 11

how many units HORIZONTALLY in the graph the "vertex" of |x| graph moved?

how many units VERTICALLY it moved?

Answer 12

up to over 2 to the left???

Answer 13

up 2

Answer 14

well, the graph shows 2 lines on the grid moved UP ,yes but it also shows the 4 there

so each grid line is 2 units

Answer 15

hmmm actaully just for "y-axis" is 2 units.. for the x-axis each grid line is just 1 unit

Answer 16

they both count by 2s though so 3 to the left and 4 up

Answer 17

yeap so it went UP by 2 units,and to the LEFT by 3 units

there's a 7 in each choice, implying it SHRUNK by a factor of +7

if it were -7 the graph would look so is +7 since it's going still UP

so 2 units UP and 3 units LEFT meaning \(\bf y=|x{\color{brown}{ +3}}|{\color{blue}{ +4}}\)

notice that -x-3 => -(x+3) or -1 * (x+3)

now the -1 INSIDE the absolute value, will play no role on shifting it or flipping it
because that will just make the value inside the parentheses negative

once we remove the bars, the negative will go back to positive anyway

so for that matter |-(x+3)| => x+3
and | x+ 3 | => x+3

thus we can say that \(\bf y=|x{\color{brown}{ +3}}|{\color{blue}{ +4}}\to |-(x+3)|+4\to |-x-3|+4\)

Answer 18

ahemm 4 units UP and 3 left that is =)