Meghan
Secondary (Gr. 12, BC)
Student

Hi there,

I have a couple questions about some function questions I got for homework.

The question reads:

Write the equations for f(x) = squareroot(4 - (x - 2)^2) after:

a) a horizontal expansion by a factor of 2
Answer: f(x) = squareroot(4 - (1/2x - 2)^2)
b) a horizontal translation 3 units left
Answer: f(x) = squareroot(4 - (x + 1)^2)
c) the expansion in part a), then the translation in part b)
d) the translation in part b), then the expansion in part a)

I understand how to do a) and b), but I'm not sure what I'm supposed to do for the equations in a specific order (expansion, then translation vs. translation, then expansion).

Thank you so much!
-Meghan

Hi Meghan,

To perform the expansion by 2 you divided the variable by 2. To perform the translation 3 units to the left you added 3 to the variable. Let me try this with a different function.

Start with g(x) = x².
Expansion by a factor of 2 gives ( ^x/₂)² = x²/4
Translation of this function 3 units to the left gives (x + 3)²/4

Start again with g(x) = x².
Translation 3 units to the left gives (x+3)²
Expansion of this function by a factor of 2 gives (^x/₂ + 3)²

Is (x + 3)²/4 = (^x/₂ + 3)²?

Penny