Question

which of the functions shown is the graph of y = x³ + 3?

Explanation:

Step1: Recall the parent function

The parent function of \( y = x^3 + 3 \) is \( y = x^3 \), which has a point at \( (0,0) \) and is a cubic curve passing through the origin, with the left end going down and the right end going up.

Step2: Analyze the transformation

The function \( y = x^3 + 3 \) is a vertical shift of the parent function \( y = x^3 \) by 3 units up. So, the point \( (0,0) \) on \( y = x^3 \) will shift to \( (0, 0 + 3)=(0,3) \).

Step3: Identify the graph

Looking at the graphs:

• The graph of \( A(x) \) passes through \( (0,3) \), has the same cubic shape (left end down, right end up) with a vertical shift up by 3.
• The other graphs ( \( B(x) \) and \( C(x) \)) do not have the point \( (0,3) \) or have different shapes (like \( B(x) \) seems to pass through near \( (0,0) \) initially and \( C(x) \) has a different vertical shift or shape). So the graph of \( y = x^3 + 3 \) is \( A(x) \).

Answer:

The function \( A(x) \) (the pink - colored graph) is the graph of \( y = x^3+3 \).