Question

unit 7 review: cube & cube root
which of the functions
shown is the graph of
y = x³?
a(x) b(x) c(x)

Explanation:

Step1: Recall the graph of \( y = x^3 \)

The function \( y=x^3 \) is a cubic function. Its graph passes through the origin \((0,0)\). For negative \( x \)-values, \( y = x^3 \) is negative (since a negative number cubed is negative), and for positive \( x \)-values, \( y = x^3 \) is positive (since a positive number cubed is positive). Also, the graph of \( y = x^3 \) has a point - symmetric property about the origin.

Step2: Analyze the given graphs

• For \( A(x) \) and \( B(x) \): These graphs seem to be even - function - like (symmetric about the \( y \)-axis), which is the property of quadratic functions (like \( y = x^2 \) or \( y = ax^2+bx + c,a

eq0 \)) or other even - degree functions. Their graphs are symmetric about the \( y \)-axis, and for negative \( x \)-values, the \( y \)-values are positive (similar to \( y=x^2 \) where \( (-x)^2=x^2 \)). But for \( y = x^3 \), when \( x=-1 \), \( y=-1 \), so the graph should be in the third quadrant (negative \( x \), negative \( y \)) for negative \( x \)-values.

• For \( C(x) \): When \( x \) is negative, \( y \) is negative (since it goes into the third quadrant), and when \( x \) is positive, \( y \) is positive (goes into the first quadrant), and it passes through the origin. Also, the shape of the graph of \( C(x) \) matches the general shape of the cubic function \( y = x^3 \) (slowly increasing for large \( x \), passing through the origin, and having the correct sign behavior for positive and negative \( x \)).

Answer:

\( C(x) \)