Question

Which of the following could be the graph of f(x)=a(x+b)^1/3 if both a and b are positive numbers? See attached pictures for answer choices!

Answer 1

We have to know some little things about the function before actually choosing any answer.

Answer 2

what do you mean @Owlcoffee ? this is all that the problem says

Answer 3

We'll give a and b any positive values, so we can study the function.
say a=1 and b=2
The function would look like this:
\[f:f(x)=a(x+b)^{\frac{ 1 }{ 3 }}\]

Answer 4

Find out what the x and y intercepts are for the function and see which choice is compatible with those intercepts.

Answer 5

Then applying the values i said, we'll have:
\[f:f(x)=(x+2)^{\frac{ 1 }{ 3 }}\]

Answer 6

Now that we re-built our function let's find the roots, with that I mean when x=0
\[f:f(0)=(0+2)^{\frac{ 1 }{ 3 }}\]

Answer 7

When x = 0, y = a * b^(1/3) Since a and b are positive, the graph should cut the y axis on the positive side.

When x = -b, y = 0. Since b is positive, -b will be negative and so the graph should cut the x axis on the negative side.

Which choice represent positive y intercept and negative x intercept?

Answer 8

would choice A represent a positive y interept and a negative x intercept?

Answer 9

Yes.

Answer 10

It is not asked here but you can even find a and b from the graph.

Answer 11

thank you :)

Answer 12

Welcome.