Question

The red graph (1) is the graph of f(x) = 2x. Describe the transformation of the blue function (2) and write the equation of the graph.

Answer 1

any ideas ?

Answer 2

well it shifts to the right and up

Answer 3

yes. any numbers ?

Answer 4

shifts up 2 and right 1?

Answer 5

yes, up 2. but to the right more than 1 step.

if you shifted the blue curve down two, its left part would match the red, but it curves up much later. Find the spot where the red curve first hits y=+1
now find the same spot on the blue curve where it goes up 1 step. what x is that ?

Answer 6

5

Answer 7

yes. the red curve is at x=0 when it reaches y up by 1 step.
the blue curve is at x=5 when it goes up by 1 step.
that is 5 units to the right.

so your shifts are 2 up and 5 to the right

how do you do a 5 to the right ? you replace x with ?

Answer 8

x - 5

Answer 9

and the new equation is ?

Answer 10

\[y = 2^{x - 5} + 2\]

Answer 11

as a check, when x=6, the blue curve has y= 4

checking: 2^(6-5) +2
= 2^1 +2
= 2+2= 4. looks good.

Answer 12

i think you literally have saved my life

Answer 13

i have 3 left

Answer 14

ok

Answer 15

The red graph (1) is the graph of f(x) = log(x). Describe the transformation of the blue function (2) and write the equation of the graph.

Answer 16

up and to the left?

Answer 17

definitely

Answer 18

left 2 up 1?

Answer 19

it is up 1. if you are having trouble with the left/right amount.
first apply the up 1 shift to the red curve. at a few points.

then see if you can see how far the blue curve is shifted right or left

Answer 20

left -1?

Answer 21

or -2

Answer 22

yes , though I would say shifted -1 or shifted left (but not both)

notice if you move the point (1,0) on the red curve up 1, you get (1,1)
now how far do you move left to get to the blue curve at (0,1) ?

Answer 23

i have no idea.