Question

cubic & cube root functions unit online practice
complete this assessment to review what you’ve learned. it will not cour
what is the inflection point of $f(x) = (x + 7)^3 - 3$? (1 point)
\\(\circ\\) \\((-7, 3)\\)
\\(\circ\\) \\((7, 3)\\)
\\(\circ\\) \\((7, -3)\\)
\\(\circ\\) \\((-7, -3)\\)

Explanation:

Step1: Recall the parent function

The parent function of a cubic function is \( y = x^3 \), which has an inflection point at \( (0,0) \).

Step2: Analyze the transformations

For the function \( f(x)=(x + 7)^3-3 \), we have a horizontal shift and a vertical shift.

• The horizontal shift: \( x\to x + 7 \) means the graph is shifted 7 units to the left. So the x - coordinate of the inflection point of the parent function \( x = 0 \) will be shifted to \( x=0 - 7=-7 \).
• The vertical shift: \( y\to y-3 \) means the graph is shifted 3 units down. So the y - coordinate of the inflection point of the parent function \( y = 0 \) will be shifted to \( y = 0-3=-3 \).

Answer:

\((-7, - 3)\) (corresponding to the option: \((-7,-3)\))