Function Notation and Substitution Concepts

The video tutorial explores the concept of functions, differentiating them from non-functions using examples like circles. It introduces function notation, explaining how y is a function of x, and discusses the importance of context in understanding mathematical notation. The tutorial provides examples to illustrate how to apply function notation, including substituting values and using other functions as inputs.

What is the primary difference between a function and a random equation?

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

• A function has a unique output for each input.

• A random equation has no graph.

• A random equation always forms a straight line.

Why is a circle not considered a function?

• It is a straight line.

• It can have more than one output for a single input.

• It has no graph.

• It has only one output for each input.

What is the visual test to determine if a graph is not a function?

• The graph is a circle.

• A vertical line intersects the graph more than once.

• The graph has no intersections.

• The graph is a straight line.

In function notation, what does 'y is a function of x' imply?

• y depends on the value of x.

• y is always greater than x.

• x depends on the value of y.

• x is always greater than y.

What does the notation y(x) typically indicate?

• y is multiplied by x.

• y is a function of x.

• x is a function of y.

• y and x are unrelated.

How can you determine the meaning of a notation like y(x)?

• By assuming it is always addition.

• By assuming it is always multiplication.

• By looking at the surrounding context.

• By checking if x is greater than y.

What happens when you substitute x = 5 into the function y = 3x - 1?

• y = 13

• y = 16

• y = 15

• y = 14

If f(t) = 3t + 4, what is f(-1)?

• f(-1) = 0

• f(-1) = 7

• f(-1) = 1

• f(-1) = -1

What does it mean to substitute a pronumeral into a function?

• Replace the variable with a constant.

• Replace the variable with another variable.

• Replace the variable with a number.

• Replace the variable with a function.

What is the result of substituting a + 7 into the function y = 3x - 1?

• 3a + 20

• 3a + 21

• 3a + 19

• 3a + 18