Question

Match each function formula with the corresponding transformation of the parent function y = 3 x

1. y = 3-x Reflected over the x-axis

2. y = 3x + 1 Reflected over the y-axis

3. y = -3x Translated down by 2 units

4. y = 3x + 1 Translated left by 1 unit

5. y = 3x - 2 Translated right by 2 units

6. y = 3x - 2 Translated up by 1 unit

Answer 1

We are given the parent function,
`y=3^x`.

So, we have,

1. Reflection over x-axis. 2. Reflection over y-axis.

This changes f(x) to -f(x). This changes f(x) to f(-x)

New function is,
`y=-3^x` New function is
`y=3^(-x)`

3. Translated down by 2 units 4. Translated left by 1 unit

This changes f(x) to f(x)-2 This changes f(x) to f(x+1)

New function is,
`y=3^x-2` New function is,
`y=3^(x+1)`

5. Translated right by 2 units 6. Translated up by 1 unit

This changes f(x) to f(x-2) This changes f(x) to f(x)+1

New function is
`y=3^(x-2)` New function is,
`y=3^(x)+1`