What is a one-to-one mapping?

A one-to-one mapping is a transformation where each input is mapped to exactly one unique output , and no two inputs are mapped to the same output .

True or False? A many-to-one mapping can be a function .

True. A many-to-one mapping can be a function .

What is the vertical line test ?

The vertical line test is a method to determine if a graph represents a function . If a graph does represent a function , then any vertical line should intersect with the graph once at most .

What is the domain of a function?

The domain of a function is the set of values that are used as inputs for the function.

What is the range of a function?

The range of a function is the set of values that are given as outputs by the function.

True or False? An inverse function reverses the effect of a function .

True. An inverse function reverses the effect of a function .

True or False? Only a many-to-one function has an inverse function.

False. A many-to-one function does not have an inverse function. Only one-to-one functions have inverses .

What is the horizontal line test ?

The horizontal line test is a method to determine if a function has an inverse . If a function has an inverse , then any horizontal line should intersect with the graph once at most .

What is the relationship between the domain of a function and its inverse function ?

The domain of a function becomes the range of its inverse function .

What is the difference between the command terms ' draw ' and ' sketch ' when graphing?

To sketch : show the general shape of the graph and label key points and axes. To draw : use a pencil and ruler to draw the graph to scale, plot points accurately, join points with a smooth curve or a straight line, and label key points and axes.

An asymptote is a line which the graph will get closer and closer to but not touch .

True or False? Most GDC models will automatically plot asymptotes .

False. Most GDC makes/models will not plot or show asymptotes just from inputting a function.

Define local minimum ( maximum ).

A local minimum ( maximum ) is a point at which the graph reaches the minimum ( maximum ) value that it takes in the immediate vicinity of the point. The graph may reach lower (higher) values further away from the point. It is also called a turning point .

True or False? A local minimum / maximum is always the global minimum / maximum of a function.

False. A local minimum / maximum is not necessarily the global minimum / maximum (the minimum/maximum of the whole graph).

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Cards in this collection (25)

What is a one-to-one mapping?
A one-to-one mapping is a transformation where each input is mapped to exactly one unique output, and no two inputs are mapped to the same output.
True or False?
A many-to-one mapping can be a function.
True.
A many-to-one mapping can be a function.
What is the vertical line test?
The vertical line test is a method to determine if a graph represents a function.
If a graph does represent a function, then any vertical line should intersect with the graph once at most.
What is the domain of a function?
The domain of a function is the set of values that are used as inputs for the function.
What is the range of a function?
The range of a function is the set of values that are given as outputs by the function.
What symbol is used to represent the set of all real numbers?
$ℝ$ represents the set of all real numbers (i.e. all the numbers that can be placed on a number line).
What does $ℚ$ represent?
$ℚ$ represents the set of all rational numbers, $\frac{a}{b}$ , where $a$ and $b$ are integers and $b \neq 0$ .
What is a composite function?
A composite function is a function made up of two or more functions. One function is applied to another function, e.g. $(f \circ g) (x)$ .
True or False?
The order in which the functions in a composite function are applied does not matter.
False.
The order in which the functions in a composite function are applied does matter. $(f \circ g) (x)$ is not usually equivalent to $(g \circ f) (x)$ .
Always apply the function closest to the variable first.
E.g. for the composite function $(f \circ g) (x)$ , you must first apply the function $g$ followed by the function $f$ .
To find the domain and range of a composite function, what is the first step you need to take?
To find the domain and range of a composite function, the first step is you need to take is to find the range of the first function that is applied.
E.g. To find the domain and range for the function $(f \circ g) (x)$ , you must first find the range of $g$ .
True or False?
An inverse function reverses the effect of a function.
True.
An inverse function reverses the effect of a function.
True or False?
Only a many-to-one function has an inverse function.
False.
A many-to-one function does not have an inverse function.
Only one-to-one functions have inverses.
What is the horizontal line test?
The horizontal line test is a method to determine if a function has an inverse.
If a function has an inverse, then any horizontal line should intersect with the graph once at most.
What is the relationship between the domain of a function and its inverse function?
The domain of a function becomes the range of its inverse function.
State the relationship between the graphs of $f (x)$ and $f^{- 1} (x)$ .
The graph $y = f^{- 1} (x)$ is a reflection of the graph $y = f (x)$ in the line $y = x$ .
How is continuity determined in piecewise functions?
Continuity in piecewise functions is determined by checking whether the function values match at the boundaries between intervals.
E.g. The piecewise function $f (x) = \{\begin{cases} x + 8 & 2 < x \leq 5 \\ 4 x - 7 & 5 < x \leq 10 \end{cases}$ is continuous, because at the boundary between the two intervals, $x = 5$ , the output is the same: $(5) + 8 = 13$ and $4 (5) - 7 = 13$ .
What is the identity function?
The identity function maps each value in a function to itself.
$id (x) = x$ .
If two composite functions, $f \circ g$ and $g \circ f$ , have the same effect as the identity function, what can be said about the functions $f$ and $g$ ?
If two composite functions, $f \circ g$ and $g \circ f$ , have the same effect as the identity function, then the functions $f$ and $g$ must be inverse functions of each other.
How do you determine if a point $(a, b)$ lies on the graph $y = f (x)$ ?
A point $(a, b)$ lies on the graph $y = f (x)$ if $f (a) = b$ .
What is the difference between the command terms 'draw' and 'sketch' when graphing?
To sketch: show the general shape of the graph and label key points and axes.
To draw: use a pencil and ruler to draw the graph to scale, plot points accurately, join points with a smooth curve or a straight line, and label key points and axes.
Define asymptote.
An asymptote is a line which the graph will get closer and closer to but not touch.
True or False?
Most GDC models will automatically plot asymptotes.
False.
Most GDC makes/models will not plot or show asymptotes just from inputting a function.
How can you use graphs to solve the equation $f (x) = a$ ?
Plot the graphs $y = f (x)$ and $y = a$ on your GDC, and find the points of intersection.
The x-coordinates are the solutions of the equation.
Define local minimum (maximum).
A local minimum (maximum) is a point at which the graph reaches the minimum (maximum) value that it takes in the immediate vicinity of the point. The graph may reach lower (higher) values further away from the point.
It is also called a turning point.
True or False?
A local minimum/maximum is always the global minimum/maximum of a function.
False.
A local minimum/maximum is not necessarily the global minimum/maximum (the minimum/maximum of the whole graph).