Question

identify a transformation of the function f(x) = x by ovbserving the equation of the function g(x) = x + a.
a horizontal shift a units to the right
a vertical stretch by a factor of a
a vertical shift a units downward
a horizontal shift a units to the left

Answer 1

i think its the last one

Answer 2

you're right

Answer 3

awesome i have a couple more questions, could you help me

Answer 4

state the various transformation applied to the base function f(x) = |x| to obtain a graph of the function g(x) = 4[|x-3| - 6]

horizontal shift of 3 units to the left, a vertical shift downward of 24 units, and a vertical stretch by a factor of 4
horizontal shift of 3 units to the right, a vertical shift downward of 24 units, and a vertical stretch by a factor of 4
horizontal shift of 12 units to the right, a vertical shift downward of 24 units, and a vertical stretch by a factor of 4
horizontal shift of 3 units to the left, a vertical shift upward of 24 units, and a vertical stretch by a factor of 4.

Answer 5

i think its either the second or third one

Answer 6

the 2nd one, \(\bf 4[|x-3| - 6] \implies 4|x-3|-24\)

A( Bx + C ) + D

A = vertical stretch
C = horizontal shift, C < 0, to the right
D = vertical shift, D < 0, down

Answer 7

Thank you!! I have two more questions left.
state the various transformations applied to the base function f(x) = x^2 to obtain a graph of the function g(x) = -2[(x-1)^2 + 3]

a reflection about the y axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right and a vertical shift downward of 6 units
a reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units
a reflection about the y axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.
a reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units.