consider-the-functions-f1x12x3f1leftxrightfrac12x3-and-f2x12x3f2leftxrightleftfr

Question

Consider the functions f1(x)=12x3f_1\left(x\right)=\$$frac12x^3$$ and f2(x)=∣12x3∣$$f_2$$\left(x\right)=\left|\$$frac12x^3$$\right|. Graph them together and describe how applying the absolute value function in f2f_2 modifies the graph of f1f_1.

Accepted Answer

The graph of ﻿f2(x)$$f_2(x)f2$$​(x)﻿ reflects the portion of ﻿f1(x)$$f_1(x)f1$$​(x)﻿ that lies in ﻿x0x\lt{0}x0﻿ region above the ﻿xxx﻿-axis.

Answer

The graph of ﻿f2(x)$$f_2(x)f2$$​(x)﻿ reflects the graph of ﻿f1(x)$$f_1(x)f1$$​(x)﻿ across yy-axis.

Answer

The graph of ﻿f2(x)$$f_2(x)f2$$​(x)﻿ reflects the graph of ﻿f1(x)$$f_1(x)f1$$​(x)﻿ across y=xy=x.

Answer

The graph of ﻿f2(x)$$f_2(x)f2$$​(x)﻿ reflects the portion of ﻿f1(x)$$f_1(x)f1$$​(x)﻿ that lies in x≥0x\geq{0} region above the ﻿xxx﻿-axis.

Consider the functions f1(x)=12x3f_1\(\left\)(x\(\right\))=\(\frac\)12x^3 and f2(x)=∣12x3∣f_2\(\left\)(x\(\right\))=\(\left\)|\(\frac\)12x^3\(\right\)|. Graph them together and describe how applying the absolute value function in f2f_2 modifies the graph of f1f_1.

Consider the functions $f sub 1 of x equals one half x cubed$ and $f_{2} (x) = ∣ \frac{1}{2} x^{3} ∣$ . Graph them together and describe how applying the absolute value function in $f sub 2$ modifies the graph of $f sub 1$ .