Question

write a function for each graph described as a transformation of y=x^2

a. y=x^2 undergoes a shift left of 2 units, then a reflection through the x-axis.

b. y=x^2 undergoes a horizontal stretch by a factor of 1/3, then a shift up of 4 units.

Answer 1

so in the other problem we went from an equation to a description, this time we are simply going in the opposite direction

Answer 2

for the first problem we will first circle the lines in the table that match the description

Answer 3

first we will replace "x" with "x+2" (be careful with parentheses) and then write a negative sign in front, outside the parentheses

Answer 4

so f-(x+c)

Answer 5

f-(x+2)

Answer 6

negative sign needs to be in front ^^ also we must use the function in the problem which is y = x^2

Answer 7

y = -(x+2)^2 = your ans

see if you can try the second problem (b) using a similar line of logic

Answer 8

keep in mind: f(x) is what's inside the table, it's just an example of how to do it. the problem uses y = x^2 so your final answer should have y and some form of x^2 in the answer

Answer 9

so f (ax)

Answer 10

and f(x) +c

Answer 11

good, now try to replace a and c with the numbers given in the problem ^^

Answer 12

y=1/3x^2

Answer 13

:/

Answer 14

if (1/a) = (1/3) what is a?

Answer 15

3

Answer 16

SO 3X^2

Answer 17

good so the stretch becomes y = (3x)^2 (the 3 needs to be inside the parentheses)

the transformation up by 4 just adds 4 to the outside

so y = (3x)^2 + 4 = your ans

Answer 18

horizontal stretches and shrinks are the most confusing part of function transformations tbh

Answer 19

Yeah that is the part that is most confusing for me, But the table does make it easier.

THANKS!