Question

describe the transformation of parent function f(x) : h(x)=f(x-1)

Answer 1

shifts right 1 unit

Answer 2

Yup. It shifts one to the right.

Answer 3

what about g(x)=3.4f(x)

Answer 4

Every value is amplified by 3.4; or, the graph gets "bigger".

Answer 5

(But not wider.)

Answer 6

badref wouldnt that be a vertical stretch?

Answer 7

More concise way of putting it. ;D But yes, a vertical stretch is an amplification of values.

Answer 8

its a vertical stretch or so my teacher says but how do you figure this out??

Answer 9

absolute value of a is vertical stretch

Answer 10

Alright, let's say I have af(x), where for any value of f(x) I can get, it is multiplied by the scalar a, right?

Now, imagine sin(x). Multiply all values by a. Suddenly, the maximum and minimums of the function become larger in magnitude.

Answer 11

whats scalar a?

Answer 12

Just "a".

Answer 13

so for example k(x)=-f(x) would be moving to the left?

Answer 14

nooope that - would just reflect over x axis

Answer 15

Redlinl knows his stuffs.

Answer 16

I have a test tomorrow, if there was a way you could explain to me how to describe the transformation of parent functions I would HIGHLY appreciate it :D

Answer 17

inside parenthesis is a phase shift(+ is left, - is right) and the coefficient in front of the x in the parentheses must be 1 so factor if needed. The number in front of the parenthesis is a. absolute value(a) is the vertical stretch if greater than 1 or vertical compression if less than one. IF the a is negative reflect over x axis. IF there is a plus or minus outside of the parenthesis than it tells you to go down or up (+) is up (-) is down. sorry im bad at explainin

Answer 18

Sure. Imagine any function f(x), okay? Now, let's examine some transformations.

f(x-a) shifts f(x) over to the right by a. All inputted x values have a subtracted from them, meaning that the x values must be higher to look like the original function.

f(x+a) shifts f(x) over to the left by a. All inputted x values have a added to them, meaning the x values must be lower to look like f(x).

f(-x) flips the graph over the y-axis. All inputted x values resemble their negative counterpart, causing the graph to "flip", since now the positive quadrant(s) look like the negative quadrant(s), and vice versa.

-f(x) flips the graph over the x-axis. All positive values of x are now negative, and vice versa.

af(x) amplifies each value of f(x), so for every x, the corresponding f(x) now seems to be multiplied by a. Whether this is larger or smaller is dependent on a being a>1 or 0<a<1.

f(ax) "distorts" the graph. Now, every x value is treated as ax instead. This is a complicated effect, but generally just remember that all x values are magnified (bigger or smaller depends on a).

Answer 19

dont forget though when doing f(x+a) or f(x-a) the coefficient in front of x MUST be 1 so factor it out to make it 1 if needed

Answer 20

Yes, very good point.

Answer 21

Oh thank you so much! I am looking at some problems to see if I understand