Math Problem Statement
Which of the following is a domain restriction on the quadratic parent function that makes it one-to-one?
Which of the following is a domain restriction on the quadratic parent function that makes it one-to-one?
D: (−∞, 0) ∪ (0, ∞)
There is no domain restriction needed.
D: {x|x < 1}
D: [0, ∞)
Solution
The quadratic parent function is not inherently one-to-one because it fails the horizontal line test; for every -value, there can be two corresponding -values. However, it can be made one-to-one by restricting its domain.
Out of the given options, the correct domain restriction that makes the quadratic parent function one-to-one is:
D: [0, ∞)
This restricts the domain to non-negative -values, ensuring that the function passes the horizontal line test because every output corresponds to exactly one input .
Why the other options don't work:
- D: (−∞, 0) ∪ (0, ∞) — This still includes two different -values that can yield the same -value, so it does not make the function one-to-one.
- There is no domain restriction needed. — This is incorrect because, without a restriction, the quadratic function is not one-to-one.
- D: {x|x < 1} — While this restricts the domain, it still allows negative -values, which cause the function to fail the horizontal line test.
Would you like more details or have any further questions?
Here are 5 related questions for further exploration:
- What is the definition of a one-to-one function?
- How do you apply the horizontal line test to check if a function is one-to-one?
- What is the range of the quadratic function when its domain is restricted to ?
- How can the inverse of a quadratic function be found if the domain is restricted?
- What transformations can affect whether a function is one-to-one?
Tip: When restricting domains, focus on isolating sections where the function is monotonic (strictly increasing or decreasing).
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Functions
Quadratic Parent Function
One-to-One Functions
Formulas
Quadratic Function f(x) = x^2
Theorems
Horizontal Line Test
Suitable Grade Level
Grades 9-12
Related Recommendation
Determining Inverses of Quadratic Functions: One-to-One and Function Inverses
Limiting the Domain of f(x) = x^2 - 5 for a One-to-One Function
Determine if a Parabola Represents a One-to-One Function
Domain Restriction for One-to-One Function with f(x) = (x + 3)^2
Determining the Domain Restrictions for Function Invertibility