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)).

Tags

CCSS.8.F.A.1

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.

Tags

CCSS.8.F.A.1

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.8.F.A.1

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.

Tags

CCSS.HSF.IF.A.2

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.