FREE Pre-Calculus Functions Questions and Answers

Question 1

What is an even function defined as?

Accepted Answer

A function f is even if f(−x)=f(x), for all x in the domain of f.

Answer

An even function is characterized by its symmetry about the y-axis. Mathematically, a function f is considered even if substituting -x for x in the function's expression results in the original function, i.e., f(-x) = f(x). This property means that points (x, y) and (-x, y) both lie on the graph of the function.

Question 2

How would you define an odd function?

Accepted Answer

A function f is odd if f(−x)=−f(x), for all x in the domain of f.

Answer

An odd function exhibits rotational symmetry about the origin. Its definition states that if you replace x with -x in the function, the result is the negative of the original function, expressed as f(-x) = -f(x). This means that if (x, y) is a point on the graph, then (-x, -y) is also a point on the graph.

Question 3

Which of these indicate that a function is one-to-one or not?

Accepted Answer

Horizontal Line Test

Answer

The Horizontal Line Test is used to determine if a function is one-to-one. If any horizontal line intersects the graph of a function at most once, then the function is one-to-one. This means that each output (y-value) corresponds to exactly one input (x-value).

Question 4

What test shows if a relationship is a function or not?

Accepted Answer

Vertical Line Test

Answer

The Vertical Line Test is a graphical method used to determine if a given relation is a function. If any vertical line drawn through the graph intersects the relation at more than one point, then the relation is not a function. This is because a function must assign exactly one output (y-value) to each input (x-value).

Question 5

What does the composition of functions mean?

Accepted Answer

An operation (fog)(x) that is equal to f (g(x)).

Answer

The composition of functions, denoted as (f o g)(x) or f(g(x)), is an operation where one function is applied to the result of another function. Essentially, the output of the inner function (g(x)) becomes the input for the outer function (f). This creates a new function that combines the actions of both original functions.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

FREE Pre-Calculus Functions Questions and Answers