Function Domain and Range Quiz

10 Questions

What is the vertex of the parabola representing the water flow from the sprinkler?

(3, 4.5)

What does the negative sign attached to the squared variable indicate about the parabola?

It opens downwards

What does finding the roots of the parabola help determine?

The x-intercepts

What does the maximum height of the water, 4.5 feet from the ground, represent in the graph of the function?

The y-coordinate of the vertex

What is the definition of a function in math?

A function is an expression that describes the relationship between an independent variable and a dependent variable, with only one output for every input.

What does the notation $f(x)$ represent in a function?

The dependent variable or output of the function.

In the function $f(x) = x^2 + 3x - 5$, what does the variable $x$ represent?

The input value or independent variable.

What is the domain of the function $f(x) = rac{1}{(x-2)(x+3)}$?

All real numbers except 2 and -3

Which type of function has a graph representing a constant rate of change?

Linear function

What is the range of the function $g(x) = x^2 - 4x + 4$?

$ ext{Range} = ext{All real numbers} ext{ such that } y ext{ satisfies } y ext{ is greater than or equal to } 0$

Study Notes

Function Domain and Range Summary

The domain of a function is the set of all possible input values, while the range is the set of all possible output values.
A function's domain can be restricted by rules such as avoiding zero in a denominator or negative numbers under an even radical.
Functions can be graphed on a coordinate plane by choosing input values, calculating outputs, and plotting points.
Linear functions are in the form y = mx + b and have a graph that is a straight line representing constant rate of change.
Non-linear functions have graphs that follow specific patterns, such as parabolas for even exponent functions and up-down-up or down-up-down patterns for odd exponent functions.
The graph of a function can reveal its domain and range.
Example 1: The linear function f(x) = 2x + 3 has a graph that is a straight line with a domain and range of all real numbers.
Example 2: The non-linear function g(x) = 1/(x-3) has a graph that is a curve with a domain of all real numbers except 3 and a range of all real numbers except 0.
Example 1: A function f(h) = 12h + 25 represents the amount a student can earn per week with a domain of 0 <= h <= 40 and a range of $25 to $505 per week.
Example 2: The height of water from a sprinkler is a function with time as the independent variable and height as the dependent variable, following a parabolic path.
The height function of the water from the sprinkler can be graphed to show its path over time.
The domain and range of a function can have real-world context, such as the hours worked for earnings or time released for water height.