Function Notation and Operations

The video tutorial explores the concept of functions, distinguishing them from random equations. It introduces visual and technical tests to identify functions, explains function notation, and demonstrates how to use it with various inputs. The tutorial also covers substitution in functions and working with nested functions, providing a comprehensive understanding of these mathematical concepts.

What is the primary difference between a function and a non-function?

• A function is always a straight line.

• A function has a unique output for each input.

• A function is always a circle.

• A function can have multiple outputs for a single input.

Why is a circle not considered a function?

• It has more than one output for some inputs.

• It is a closed shape.

• It is a 3D object.

• It is a type of graph.

What does the notation y(x) signify?

• y is added to x.

• y is subtracted from x.

• y is multiplied by x.

• y is a function of x.

In function notation, what does the context help determine?

• The size of the graph.

• The type of graph.

• The color of the graph.

• Whether the notation refers to a function or an algebraic expression.

If f(t) = 3t + 4, what is f(2)?

• 12

• 10

• 8

• 6

What does substituting a value into a function involve?

• Dividing the function by the value.

• Adding the value to the function.

• Replacing the variable with the given value.

• Multiplying the function by the value.

What is the result of substituting x = 5 into the function y = 3x - 1?

• 15

• 14

• 16

• 13

How do you interpret f(y(x)) in terms of function operations?

• f is applied to the result of y(x).

• f is added to y(x).

• f is subtracted from y(x).

• f is multiplied by y(x).

What does it mean to combine functions?

• Multiplying two functions together.

• Subtracting one function from another.

• Adding two functions together.

• Using the output of one function as the input of another.

What is the result of expanding the expression 3(a + 7) - 1?

• 3a + 20

• 3a + 18

• 3a + 21

• 3a + 19