5.1: Intro to Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every input value (x), there is one and only one output value (f(x)).

Front

What is not a function?

Back

A relation is not a function if at least one input value (x) is associated with more than one output value.

Front

Evaluate the function f(x) = x^2 - 2 for x = 5.

Back

f(5) = 5^2 - 2 = 25 - 2 = 23.

Front

Which of the following sets of values represents a function? (9,5) (10,5) (9,-5) (10,-5), (3,4) (4,-3) (7,4) (3, 8), (6,-5) (7, -3) (8, -1) (9, 1), (2, -2) (5, 9) (5, -7) (1, 4)

Back

(6,-5) (7, -3) (8, -1) (9, 1) is a function because each input has a unique output.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve at more than one point, then the curve is not a function.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (f(x)) that the function can produce.

Front

If f(x) = 3x + 1, what is f(2)?

Back

f(2) = 3(2) + 1 = 6 + 1 = 7.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.