Question
the graph of a quadratic function f is shown on the grid. which of these best represents the domain of f?
a -4 < x < 5
b y > -12.25
c all real numbers
d all real numbers less than -4 or greater than 5
a -4 < x < 5
b y > -12.25
c all real numbers
d all real numbers less than -4 or greater than 5
Answers
GPT-4o mini
The domain of a quadratic function is generally all real numbers since a quadratic function typically extends infinitely in both the left and right directions on the graph.
Looking at the options:
a) -4 < x < 5 would restrict the domain to only the values between -4 and 5, which is not characteristic of typical quadratic functions.
b) y > -12.25 does not represent the domain; it describes a range of the function's values (the range would be the set of possible y-values).
c) All real numbers: This is usually the correct choice for the domain of a quadratic function.
d) All real numbers less than -4 or greater than 5 would also restrict the domain incorrectly since many quadratic functions have x-values beyond -4 and 5.
Thus, the best representation of the domain of the quadratic function f is **c) all real numbers**.
Looking at the options:
a) -4 < x < 5 would restrict the domain to only the values between -4 and 5, which is not characteristic of typical quadratic functions.
b) y > -12.25 does not represent the domain; it describes a range of the function's values (the range would be the set of possible y-values).
c) All real numbers: This is usually the correct choice for the domain of a quadratic function.
d) All real numbers less than -4 or greater than 5 would also restrict the domain incorrectly since many quadratic functions have x-values beyond -4 and 5.
Thus, the best representation of the domain of the quadratic function f is **c) all real numbers**.