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Math Practice

Parent Functions Practice Problems

Strip away the numbers that stretch and shift a graph, and name the parent that is left. The later problems use what the parent tells you about domains, ranges, starting points and asymptotes.

  1. 1.

    What is the parent function of ?

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    is squared; the 3, the and the only transform it. Parent: .

  2. 2.

    What is the parent function of ?

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    is inside absolute value bars, so the parent is , shifted 5 left and 2 down.

  3. 3.

    What is the parent function of ?

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    is under a square root, so the parent is , shifted 3 right.

  4. 4.

    What is the parent function of ?

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    is cubed, so the parent is , stretched by 2, flipped and shifted 1 up.

  5. 5.

    What is the parent function of ?

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    is in the denominator, so the parent is the reciprocal , stretched by 4 and shifted 1 left.

  6. 6.

    What is the parent function of ? (Type cbrt(x) for a cube root.)

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    is under a cube root, so the parent is .

  7. 7.

    What is the domain of the parent function ? Use interval notation (type oo for ∞).

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    Square roots of negative numbers aren’t real, so the domain is , or .

  8. 8.

    What is the range of the parent function ? Use interval notation.

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    A square is never negative, and every non-negative number is a square, so the range is .

  9. 9.

    The parent is shifted 2 right and 3 down. Where does the new graph start? Give the point.

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    The starting point moves 2 right and 3 down to .

  10. 10.

    What is the vertical asymptote of ? Type x = ….

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    The parent’s asymptote moves 5 right.

  11. 11.

    What is the horizontal asymptote of ? Give the y-value.

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    The parent has asymptote ; subtracting 4 moves it to .

  12. 12.

    The point is on . Where does it move on the graph of ? Give the point.

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    The graph shifts 3 left and 2 down, so moves to .
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MPhil in Mathematics, Founder of Mathovia
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Parent Functions Practice Problems

These problems follow the parent functions lesson. In each equation, look past the transformations to the operation on .

The general form

Common mistakes to watch for

  • Confusing and shapes. The quadratic is a U with both ends up; the cubic rises on the right and falls on the left.
  • Wrong domain for roots and logs. needs and needs .
  • Forgetting asymptotes. has asymptotes at and ; approaches on the left.
  • Shifting the wrong way. Inside the function, moves the graph 3 to the right, not left.

Frequently Asked Questions

How do I type a parent function?+

Use x^2, x^3, |x|, sqrt(x), cbrt(x) or 1/x. Words such as quadratic or square root are accepted too.

How do I identify the parent function?+

Ignore the number in front, the number added inside, and the number added outside. Whatever is still being done to x tells you the parent.

How do I type intervals and points?+

Write intervals with brackets and oo for infinity, like [0, oo). Write points as (2, -3).

More practice problems

Function Notation Practice Problems Domain and Range Practice Problems Piecewise Functions Practice Problems