Explain why the vertical line test is used to determine if a graph represent a function

Vertical line test tells us whether the graph represents a function or not. This test states that "if a vertical line intersects the graph at only one point then it is a function otherwise not"

Now, if any vertical line intersects the graph at two points then it means that for a value of x, we have to y values. In other words the x value has not unique y values which doesn't satisfy the condition of a relation to be a function.

Therefore, if the vertical line intersects the graph at only point then only each x values has a unique y values.

Please see the attached images. Image 1 is not a function since the vertical line intersects at two points whereas, image 2 represents a function.

Hence, we can conclude that vertical line test is used to determine if a graph represent a function.

the highest percentage for deaths in construction from highest to lowest is as follows: falls, struck by objects, electrocution, and caught-in/between. these four are collectively known as fatal four.

in the case of falls, the type that is responsible for the overall highest death in the category is falls from roofs.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)