Understanding Zeros of Linear Functions

The video tutorial explains how to determine the zeros of two linear functions. It begins by defining a zero of a function as an x-value that results in a function value of zero. The tutorial then provides a detailed, step-by-step process for finding the zeros of two specific functions, g(x) = -10 - 5x and f(x) = 56 - 8/3x, by setting the function equal to zero and solving for x. The solutions are verified graphically by showing where the functions intersect the x-axis. The tutorial emphasizes understanding the algebraic and graphical perspectives of finding zeros.

What is a zero of a function in terms of its graph?

• A point where the graph crosses the x-axis

• A point where the graph touches the y-axis

• A point where the graph is parallel to the x-axis

• A point where the graph is parallel to the y-axis

What is the first step in finding the zero of g(x) = -10 - 5x?

• Multiply both sides by 5

• Add 10 to both sides

• Subtract 5x from both sides

• Divide both sides by -5

What is the zero of the function g(x) = -10 - 5x?

• x = 0

• x = -2

• x = 2

• x = 10

How is the zero of g(x) = -10 - 5x verified graphically?

• By checking if the graph touches the y-axis

• By checking if the graph crosses the x-axis at x = -2

• By checking if the graph is parallel to the y-axis

• By checking if the graph is parallel to the x-axis

What is the initial equation setup for finding the zero of f(x) = 56 - (8/3)x?

• 0 = 56 - (8/3)x

• 0 = 56x + 8/3

• 0 = 56 + (8/3)x

• 0 = 56x - 8/3

What is the reciprocal of (8/3) used in solving f(x) = 56 - (8/3)x?

• 3/8

• 8/3

• 1/3

• 1/8

What is the zero of the function f(x) = 56 - (8/3)x?

• x = 21

• x = -21

• x = 56

• x = 0

How is the zero of f(x) = 56 - (8/3)x verified graphically?

• By checking if the graph touches the y-axis

• By checking if the graph crosses the x-axis at x = 21

• By checking if the graph is parallel to the x-axis

• By checking if the graph is parallel to the y-axis

What does the point (21, 0) represent in the graph of f(x) = 56 - (8/3)x?

• The y-intercept

• The x-intercept

• The vertex

• The slope

What is the significance of finding zeros in linear functions?

• It helps in determining the maximum value of the function

• It helps in identifying where the function crosses the x-axis

• It helps in finding the y-intercept

• It helps in determining the slope of the function