ANSWERS
Name______________________________
Period____
Consider the following functions when answering the questions:
Constant
Linear
Quadratic
Square Root
Cube Root
Sine
PreCalculus
1.5 Parent Function Sorting Questions
Cubic
Cosine
Absolute Value
Rational
1. Which of the given functions do not have a domain as the set of all real numbers?
square root, rational
2. Which function has the domain as the set of all real numbers except 0?
rational
3. Which of the given functions have no negative numbers in their domains?
square root
4. Which of the functions has a range that is given by
| ∈ ℝ, −1 ≤
≤1 ?
sine, cosine
5. Which of the functions has a range that is given by
| ∈ ℝ,
≥0 ?
quadratic, absolute value, square root
6. Which of the given functions is discontinuous when x = 0?
rational
7. Which of the functions have a vertical asymptote of x = 0?
rational
8. Which of the functions have a horizontal asymptote of y = 0?
rational
9. Which of the following functions is increasing on the interval (−∞, ∞)?
linear, cubic, cube root
10. Which of the following functions is decreasing on the interval (−∞, 0)?
quadratic, absolute value, rational
11. Which of the functions has an absolute maximum?
sine, cosine,
12. Which of the functions has an absolute
minimum?
quadratic, absolute value, sine,
cosine, square root
13. For which function is f(0) undefined?
rational
14. Which functions do not have any x-intercepts?
rational, constant (except if f(x) = 0)
15. Which of the given functions are even functions?
constant, quadratic, absolute value,
cosine
17. For which functions does lim f ( x ) = ∞ .
x →∞
linear, quadratic, cubic,
absolute value, square root,
cube root
19. For which functions does lim f ( x ) = −∞ .
x →∞
none
16. Which of the given functions are odd functions?
linear, cubic, cube root, sine, rational
18. For which functions does lim f ( x ) = ∞ .
x →−∞
quadratic, absolute value
20. For which functions does lim f ( x ) = −∞ .
x →−∞
linear, cubic, cube root
21. For which functions does lim f ( x ) = 0 .
x →∞
rational, (constant if the function is f(x) = 0)
22. Which of the functions is concave up over the interval (−∞, ∞)?
quadratic
23. Which of the functions is concave down over the interval ( −∞,0 ) ?
cubic, rational
24. Which of the functions is concave down over the interval ( 0, ∞ ) ?
cube root, square root
25. Which of the functions has no concavity?
constant, linear, absolute value