Answer:
Graph 1
Step-by-step explanation:
Given parent function,
f(x) = x^3 + 5,
[tex]f(\frac{1}{3}) = (\frac{x}{3})^3 + 5[/tex]
[tex]\implies f(\frac{1}{3})=\frac{x^3}{27}+5[/tex]
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,
[tex]\text{As } x\rightarrow \infty, f(x)\rightarrow \infty[/tex]
[tex]\text{As } x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]
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 [tex]f(\frac{1}{3})[/tex] ( shown below )
Which is similar to graph 1.
