Question

Write the cubic equation for a graph that has been… Translated right 4 Compressed by 1/3 & relected Translated 10 down & 3 left over the x-axis Stretched by a factor of 2, Translated left 2 & down 8 Compressed by ½ and up 4 translated 4 right, & 3 down Relected across x-axis & left 7 Stretched by a factor of 7, You & your partner come up with translated up 2, & left 5 one!

Answer 1

Assuming the parent cubic is f(x) = x^3 and that “stretched/compressed” means vertical stretch/compression (and reflections are across the x-axis), the transformed cubics are:

1) Translated right 4:
y = (x − 4)^3

2) Compressed by 1/3 and reflected (across x-axis):
y = −(1/3)x^3

3) Reflected across the x-axis, translated 3 left and 10 down:
y = −(x + 3)^3 − 10

4) Stretched by a factor of 2, translated left 2 and down 8:
y = 2(x + 2)^3 − 8

5) Compressed by 1/2, up 4, then translated 4 right and 3 down (net vertical +1, right 4):
y = (1/2)(x − 4)^3 + 1

6) Reflected across the x-axis and stretched by factor 7, translated left 7:
y = −7(x + 7)^3

7) Translated left 5 and up 2 (your partner’s):
y = (x + 5)^3 + 2

If any of the “stretch/compress” items were meant as horizontal (x-direction) instead, tell me which one and I’ll rewrite that equation.