Question

On a sheet of graph paper, sketch a graph of each of the following parent functions. Clearly label each parent function with its equation and its name (e.g. “Exponential Function”).

f(x)=x

f(x)=x2

f(x)=2x

f(x)=x−−√

f(x)=x−−√3

Explain the meaning of the terms “parent function” and “function family.”
short no points and at a 6th grade level

Answer 1

On your graph paper, draw x- and y-axes and label numbers. For each graph, write the equation and its name next to the curve.

f(x) = x — Identity (Linear). Draw a straight line through (−2,−2), (−1,−1), (0,0), (1,1), (2,2).
f(x) = x^2 — Quadratic (Parabola). Draw a U-shaped curve through (−2,4), (−1,1), (0,0), (1,1), (2,4).
f(x) = 2x — Linear (Steeper line). Draw a straight line through (−2,−4), (−1,−2), (0,0), (1,2), (2,4).
f(x) = √x — Square root. Start at (0,0) and draw a curve only for x ≥ 0: (1,1), (4,2). It rises slowly to the right.
f(x) = ∛x — Cube root. S-shaped curve through (−8,−2), (−1,−1), (0,0), (1,1), (8,2). It goes through the origin and continues both left and right.

Meanings (short, simple): A parent function is the simplest version of a type of graph (like y = x^2 for all quadratics). A function family is all functions that share the same general shape (for example, y = x^2, y = 2x^2, and y = (x−1)^2 are all in the quadratic family).