Question

So I am transforming parent functions to other certain equations that apply to the description, and I'm not sure how to write them out. For example, y= the square root of X, Translate 5 units down; Vertical stretch by a factor of 3/2.

Answer 1

What do you know to do so far? Any guesses?

Parent function is.........

Answer 2

Well for the equation, it's a no go, but the parent funtion is the main function you go off of, like in my example \[ y= \sqrt{x} is the parent function.\]

Answer 3

oops

Answer 4

I'm sure you know what I means. Haha

Answer 5

y = sqrt(x)

Vertical shifts occur when we add/subtract something after the function
Vertical stretches/shrinks occur when we mult something time the function.
Horizontal shifts occur when we add/subtract from the variable

What might you guess now?

Answer 6

I might guess the point on the graph would be pulled down to -5, but still a bit foggy with the vertical stretch.

Answer 7

You have the idea about what happens with the shift. All the point of the parent graph move down 5 to create the new one. y =sqrt(x) -5

The stretch/shrink literally makes every value of the original function larger (stretch) or smaller (shrink). This happens when we mult something times the function.

so....

Answer 8

The factor 3/2 \[\frac{ 3 }{ 2 } \times -5\]

Answer 9

Or possibly the other way around.

Answer 10

So close.

y = (3/2) sqrt(x) -5
^ ^ ^
vert stretch/shrink function vertical shift

Answer 11

The trick is being able to do this with a different situation.