Understanding Graphs and Functions

The video tutorial covers plotting points on a graph, determining if relations are functions, writing function rules, and using the vertical line test to identify functions. It explains how to find coordinates, understand function definitions, and apply the vertical line test to ensure a relation is a function.

What is the x-coordinate of point A if it is 6 units to the left of the origin?

• 0

• -6

• 4

• 6

If point B has an x-coordinate of 7 and a y-coordinate of 6, what are its coordinates?

• (7, 6)

• (-7, 6)

• (7, -6)

• (6, 7)

Which of the following is NOT a characteristic of a function?

• Each input has exactly one output

• A function can be represented graphically

• An input can have multiple outputs

• Different inputs can have the same output

In a valid function, what happens if x = 1 results in both y = 5 and y = 6?

• The function is valid

• The function is invalid

• The function is quadratic

• The function is linear

What is the range of the function defined as f(x) = 7 if x = 1 or 2?

• 7

• 1 and 2

• 1

• 2

How can you simplify a piecewise function that is 1/2x for x > 0 and -1/2x for x < 0?

• By using a quadratic equation

• By using the absolute value of x

• By using a trigonometric function

• By using a logarithmic function

What is the function rule for a graph where y is half of x for positive x values?

• y = 1/2x

• y = 2x

• y = x

• y = -1/2x

What does the vertical line test determine about a graph?

• If the graph is linear

• If the graph is a function

• If the graph is quadratic

• If the graph is exponential

If a vertical line intersects a graph at two points, what does this indicate?

• The graph is a function

• The graph is not a function

• The graph is linear

• The graph is quadratic

Which of the following graphs would pass the vertical line test?

• A straight line

• A parabola opening upwards

• A circle

• A horizontal line