For each relation below:
\left\{\left(16, 14\right), \left(8, 28\right), \left( - 15 , 14\right), \left( - 20 , - 28 \right)\right\}
| x | 7 | 7 | 8 | 5 | 3 |
|---|---|---|---|---|---|
| y | 1 | 9 | 3 | 2 | 6 |
Consider the function graphed:
State the domain.
State the range.
Consider the graph of y = \sqrt[3]{ - x }:
State the domain.
State the range.
The function f \left(x\right) = \sqrt{x + 1} has been graphed below:
State the domain.
Is there a value of x in the domain that can produce a function value of - 2?
Consider the graph of the function y = f \left( x \right):
State the maximum value.
State the range.
State the domain.
The function y = \sqrt{x} has a domain of x \geq 0 and a range of y \geq 0. State the domain and range of y = \sqrt{x} - 2.
State the natural domain of the the following functions:
f \left( x \right) = \dfrac{1}{\sqrt{x}}
State the domain of the following functions using interval notation:
For each graph below, state the following using interval notation.
The domain
The range
Use the graph of f to find:
The domain.
The range.
f \left( 0 \right)
f \left( 1 \right) - f \left( 7 \right)
The graphs of f \left( x \right) = \sqrt{5 - x} and g \left( x \right) = \sqrt{x + 3} are shown below:
Find the domain of the following functions using interval notation:
f
g
f + g
f - g
f \times g
\dfrac{f}{g}
\dfrac{g}{f}
Let f \left( x \right) = \dfrac{1}{x - 3} and g \left( x \right) = \dfrac{1}{x+2}. Find the domain of the following functions using interval notation:
Let f \left( x \right) = \dfrac{2}{x - 8} and g \left( x \right) = 2 - x. Find the domain of the following functions using interval notation:
(f+g)(x)
(f \times g)(x)
(f/g)(x)
(g/f)(x)
Let f \left( x \right) = \dfrac{9}{x - 7} and g \left( x \right) = \sqrt{x - 2}.
State the domain of f \left( x \right).
State the domain of g \left( x \right).
State the domain of (ff)(x).
State the domain of (f/g)(x).
State the domain of (f-g)(x).
Find (ff)(x).
Find (f/g)(x).
Find (f-g)(x).
Consider the functions f \left( x \right) = \dfrac{4 x - 3}{x + 2} and g \left( x \right) = \dfrac{x^{2} + 6 x + 8}{x^{2} + 7 x + 10}.
Find \left(f+g\right) \left(x\right).
Find the domain of \left(f + g\right) \left(x\right).
Find \left(f\times g\right) \left(x\right).
Find the domain of \left(f \times g\right) \left(x\right).
Find \left(f/g\right) \left(x\right).
Find the domain of \left(f / g\right) \left(x\right).
Given that the domain of a function is \left(-\infty, - 6 \right) \cup \left( - 6 , 3\right) \cup \left(3, \infty\right), determine if the following could be the equation of the function:
f \left( x \right) = \dfrac{x}{\left(x + 5\right) \left(x + 6\right) \left(x - 3\right)}
f \left( x \right) = \dfrac{x + 6}{x - 3}
f \left( x \right) = \dfrac{1}{\left(x - 6\right) \left(x - 3\right)}
f \left( x \right) = \dfrac{x + 6}{\left(x + 6\right) \left(x - 3\right)}