Grade 11 Functions Review - Flashcards

Forty practice flashcards covering definitions, properties, and operations related to functions, domain/range, graphing, vertical line test, piecewise functions, and evaluating functions.

What is the definition of a function?

A function is a rule of correspondence between two nonempty sets such that to every element of the domain there corresponds one and only one element of the range.

What are the domain and range in a function?

The domain is the set of inputs; the range is the set of possible outputs (values of f(x)).

How is a function often described in terms of mapping?

As a mapping from the domain onto the range.

True or False: Every function is a relation, and not every relation is a function.

True.

Why is the set C not a function in the example?

Because two ordered pairs share the same first element (0,1) and (0,-1).

Which set from the example is a function: A = {(1,2),(2,3),(3,4),(4,5)}?

A is a function because each first element is unique.

True or False: All functions are relations.

True. All functions are relations, but not all relations are functions.

What is the Vertical Line Test?

A graph is a function if any vertical line drawn passes through the graph at exactly one point.

What does the Vertical Line Test determine?

Whether a relation is a function.

How do you graph a function from a relation?

Find all ordered pairs that satisfy f, plot them on a Cartesian plane, and draw a smooth curve through the points from left to right.

What is a piecewise function?

A function whose definition involves more than one formula on different parts of its domain.

What defines the domain partition in a piecewise function?

Different intervals or conditions, such as x ≥ 0 and x < 0.

For the piecewise function f(x) = {3x+2 for x ≥ 0; -x^2+3 for x < 0}, what is f(0) and f(-3)?

f(0) = 2; f(-3) = -6.

What is the independent variable in y = f(x)?

x.

What is the dependent variable in y = f(x)?

y (the output).

How do you evaluate a function for a given x?

Substitute the value into f(x) and simplify.

If f(x) = x^2 + 3x - 2, what is f(-3)?

-2.

If f(x) = 2x - 1, what is f(-2)?

-5.

If f(x) = x^2 + 3x - 2, what is f(0)?

-2.

If f(x) = 2x - 1, what is f(2)?

3.

What does f(x) denote in the expression f(x) is the output for input x?

The output value assigned to the input x by the function f.

How do you write the sum of two functions?

(f+g)(x) = f(x) + g(x).

How do you write the difference of two functions?

(f-g)(x) = f(x) - g(x).

How do you write the product of two functions?

(f∙g)(x) = f(x) · g(x).

How do you write the quotient of two functions?

(f/g)(x) = f(x) / g(x), with g(x) ≠ 0.

What is the domain requirement for (f+g)(x), (f−g)(x), and (f∙g)(x)?

Defined for all x in the domain common to f and g.

What additional restriction applies to (f/g)(x)?

g(x) ≠ 0.

Compute (f+g)(x) if f(x) = 2x - 1 and g(x) = 3x^3 + 6x - 4.

(f+g)(x) = 3x^3 + 8x - 5.

Compute (f+g)(x) if f(x) = 3x^2 - 4x + 5 and g(x) = 2x^3 - 6x + 2.

(f+g)(x) = 2x^3 + 3x^2 - 10x + 7.

What does the notation f(x) represent?

The output value corresponding to input x produced by the function f.

How would you express the sum of function values at a given x?

Compute f(x) + g(x) for that x.

What is the meaning of the independent variable in evaluation?

The input value selected from the domain.

What happens when you substitute x into a function during evaluation?

You replace x with the given number and simplify.

What is a graph that passes the vertical line test called?

A function.

What is the relation between a function and its domain mapping?

Each domain element is paired with exactly one output in the range.

Which sets A, B, C, D in the notes form a function and why is C not?

A, B, and D are functions; C is not because it contains (0,1) and (0,-1) with the same input 0.

What does a piecewise function require in its definition?

More than one formula, each applying on a different partition of the domain.

What is the process of evaluating a function at a specified x value?

Substitute and simplify.

What is a key difference between one-to-one vs one-to-many in the context of functions?

A function cannot be one-to-many; it requires one output per input; one-to-one and many-to-one are types of functions, while one-to-many is not a function.

How would you describe mapping a domain onto a range in simple terms?

For every input, give exactly one output.