Determine whether each relation is a function, and state its domain and range.
Determine whether each relation is a function, and state its domain and range.
\displaystyle
y = 2x + 3
Determine whether each relation is a function, and state its domain and range.
Determine whether each relation is a function, and state its domain and range.
\{(2, 7), (1, 3), (2, 6), (10, -1)\}
The height of a bungee jumper above the ground is modelled by the following data.
a) Is the relationship between height and time a function? Explain
b) What is the domain?
c) What is the range?
Determine the domain and range for each of the following and state whether it is a function:
\displaystyle
f(x) = 3x + 1
Determine the domain and range for each of the following and state whether it is a function:
\displaystyle
x^2+ y^2 = 9
Determine the domain and range for each of the following and state whether it is a function:
\displaystyle
y = \sqrt{5 -x}
Determine the domain and range for each of the following and state whether it is a function:
\displaystyle
x^2 -y = 2
Arrange the following values in order, from least to greatest:
\displaystyle
|-3|, -|3|, |5|, |-4|, |0|
Sketch the graph of each function.
\displaystyle
f(x) = |x| + 3
Sketch the graph of each function.
\displaystyle
f(x) = |x| - 2
Sketch the graph of each function.
\displaystyle
f(x) = |-2x|
Sketch the graph of each function.
\displaystyle
f(x) = |0.5x|
Determine a parent function that matches each set of characteristics.
a) The graph is neither even nor odd, and as x \to \infty
, y \to \infty
b) (-\infty, 0), and (0, \infty) are both intervals of decrease.
c) The domain is [0, \infty)
Determine algebraically if each function is even, odd, or neither.
\displaystyle
f(x) = |2x|
Determine algebraically if each function is even, odd, or neither.
\displaystyle
f(x) = (-x)^2
Determine algebraically if each function is even, odd, or neither.
\displaystyle
f(x) = x + 4
Determine algebraically if each function is even, odd, or neither.
\displaystyle
f(x) = 4x^5 +3x^3 -1
The set of characteristics describes a parent function that has been shifted. Draw a possible graph, and state whether the graph is continuous.
There is a vertical asymptote at x = 1 and a horizontal asymptote at y = 3.
The set of characteristics describes a parent function that has been shifted. Draw a possible graph, and state whether the graph is continuous.
The range is \{f(x) \in \mathbb{R} \Vert -3 \leq f(x) \leq -1\}
The set of characteristics describes a parent function that has been shifted. Draw a possible graph, and state whether the graph is continuous.
The interval of increase is (-\infty, \infty)
, and there is a horizontal asymptote at y =-10
.
Sketch a graph that has the following characteristics:
x = -3 0
, and 3
.x\in (-\infty, -2)
or x\in (2, \infty)
x\in(-2, 2)
.