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Question

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 $f sub 1$ .

Accepted Answer

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

Answer

Graph comparing f1(x) = 1/2x³ (blue) and f2(x) = |1/2x³| (red), showing how absolute value modifies f1's graph.

The graph of $f_2(x)$ reflects the graph of $f_1(x)$ across $y$ -axis.

Answer

Graph comparing f1(x) = 1/2x³ (blue) and f2(x) = |1/2x³| (red), showing how absolute value alters f1's shape.

The graph of $f_2(x)$ reflects the graph of $f_1(x)$ across $y$ .

Answer

Graph comparing f1(x) = 1/2x³ (blue) and f2(x) = |1/2x³| (red), showing how absolute value affects f1's shape.

The graph of $f_2(x)$ reflects the portion of $f_1(x)$ that lies in $y$ region above the $x$ -axis.

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.

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 $f sub 1$ .