Question

List the sequence of transformations. ()=−2(−3)^4+1

Answer 1

We have the function:

()=−2(−3)^4+1

We need to go from this equation to the parent function x^4. To do that, we first do a vertical translation of 1 unit below. That is:

Vertical translation: f(x) - 1

= −2(−3)^4

Now, we make a horizontal shift of 3 units to the left, replacing x by x + 3:

f(x + 3) + 1 = −2()^4

Horizontal shift: f(x + 3) - 1

= −2x^4

We can make a horizontal expansion if we multiply this function by 1/2:

Horizontal expansion: ( f(x + 3) - 1 ) / 2

= -x^4

Finally, we make a reflection around the x-axis by multiplying this result by -1:

x-axis reflection: -( f(x + 3) - 1 ) / 2

= x^4