Question

Suppose f (x) = x^3 + 5 . Find the graph of f (1/3 x)

Answer 1

Graph 1

Explanation:

Given parent function,

f(x) = x^3 + 5,

`f((1)/(3)) = ((x)/(3))^3 + 5`

`\implies f((1)/(3))=(x^3)/(27)+5`

Which is the polynomial function,

Having x-intercept = (-3.13, 0)

y - intercept = (0,4)

∵ The degree of the function is odd and leading coefficient is positive,

Thus, the end behaviour of the function is,

`\text{As } x\rightarrow \infty, f(x)\rightarrow \infty`

`\text{As } x\rightarrow -\infty, f(x)\rightarrow -\infty`

Now, -∞ < x < -5.13, f(x) is increasing,

-5.13 < x < 0, f(x) is increasing,

And, 0 < x < ∞, f(x) is increasing,

Hence, by the above information we can plot the graph of the function
`f((1)/(3))` ( shown below )

Which is similar to graph 1.

Answer 2

Graph 1

Explanation:

The transformed graph is a horizontal stretch of the parent function by a factor of 27 but has the same y-intercept as the parent graph.