2. use transformations to sketch the graph of the following function.\n\n$$f(x) = x^3 - 2$$
2. use transformations to sketch the graph of the following function.\n\n$$f(x) = x^3 - 2$$
Answer
Explanation:
Step1: Identify the parent function
The parent function is the cubic function $y = x^{3}$.
Step2: Identify the vertical transformation
The constant $-2$ subtracted from the function indicates a vertical shift.
Step3: Determine the shift direction
Subtracting $2$ from the output shifts the graph downward by $2$ units.
Step4: Apply transformation to key points
The origin $(0,0)$ moves to $(0,-2)$, and $(1,1)$ moves to $(1,-1)$.
Answer:
To sketch the graph of $f(x) = x^{3} - 2$, start with the parent cubic graph $y = x^{3}$ and shift every point vertically downward by $2$ units. The new inflection point is at $(0, -2)$.