Parent Functions Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Match each equation to its parent function: (a) y=−x+3y = -\sqrt{x+3}, (b) y=2x−1y = \frac{2}{x-1}, (c) y=∣x∣−4y = |x| - 4, (d) y=2x+1−3y = 2^{x+1} - 3.

Solution

  1. 1
    (a) Parent: y=xy = \sqrt{x} — reflected over xx-axis and shifted left 33.
  2. 2
    (b) Parent: y=1xy = \frac{1}{x} — vertically stretched by 22 and shifted right 11.
  3. 3
    (c) Parent: y=∣x∣y = |x| — shifted down 44.
  4. 4
    (d) Parent: y=2xy = 2^x — shifted left 11 and down 33.

Answer

(a) x,(b) 1x,(c) ∣x∣,(d) 2x\text{(a) } \sqrt{x}, \quad \text{(b) } \frac{1}{x}, \quad \text{(c) } |x|, \quad \text{(d) } 2^x
Recognizing the parent function is the first step in analyzing transformations. Look for the core operation: square root, reciprocal, absolute value, exponential, etc. All modifications (shifts, stretches, reflections) are applied to this base shape.

About Parent Functions

A parent function is the simplest, most basic version of a function family — the unshifted, unstretched, unreflected template. All other functions in the family are transformations of this parent. Memorizing parent function shapes allows rapid graphing of transformed versions.

Learn more about Parent Functions →

More Parent Functions Examples

Example 1 easy

Identify the parent function of [formula] and describe the transformations.

Example 3 medium

Sketch the key features (domain, range, intercepts, asymptotes) of the parent function [formula].

Example 4 hard

Write a single equation using transformations of the parent function [formula] that has domain [form

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