Write a rule for g if g is a horizontal shrink by a factor of 5/6, followed by a translation 10 units to the left of the graph of f(x) = cube root of 15x+1.

Answer 1

Hi Natalia,

Horizontal shrinks/stretches are represented by f(ax) where is the value that result in the shrink (if it's a number greater than 1) or a stretch (if it's a number between 0 and 1).

Horizontal translations to the left are represented by f(x+a) where a is a positive number.

I believe your original function is: cube root(15x-1), where the 15x-1 is all under the root.

We can look at this as the cube root [15(x-1/15)]

Now to apply the transformations. You were asked to shrink the graph horizontally by 5/6. 5/6 is a number between 0 and 1 so this would actually stretch the graph! We need to flip the fraction and use 6/5. Recall from the rule that a horizontal shrink is represented by multiplying the x by the value, so:

cube root [15*6/5(x-1/15)]

You were also asked to shift the graph left 10 units. In order to do so, we would need to add 10 to the x, so:

cube root [15*6/5(x-1/15+10)]

Now we can simplify:

cube root [18(x+149/15)]

Distribute the 18:

cube root (18x+894/5)

Hope this helps!