Understanding Limits and Slopes

The video tutorial explains how to find the limit of the function g(x) = -4x + 7 as x approaches -1. It begins by visualizing the line and its slope, then plots points to calculate the slope between them. The tutorial emphasizes the constant slope of the line, which is -4, and demonstrates how to solve the limit problem both graphically and algebraically.

What is the function g(x) defined as in the video?

• g(x) = 4x + 7

• g(x) = -4x + 7

• g(x) = 4x - 7

• g(x) = -4x - 7

What is the y-intercept of the line represented by g(x)?

• -4

• 11

• 0

• 7

What is the slope of the line g(x)?

• -7

• 7

• -4

• 4

What is the expression for the slope between an arbitrary point and a specific point on the line?

• (g(x) - g(-1)) / (x + 1)

• (g(x) + g(-1)) / (x - 1)

• (g(x) + g(-1)) / (x + 1)

• (g(x) - g(-1)) / (x - 1)

What is the constant slope of the line as x approaches -1?

• -4

• 7

• 4

• 0

How does the slope behave as x approaches -1 from either direction?

• It becomes positive.

• It remains constant at -4.

• It fluctuates.

• It becomes zero.

What is the algebraic expression for g(x) when x approaches -1?

• -4x + 11

• -4x + 7

• -4x - 11

• -4x - 7

What is the result of factoring the numerator in the algebraic approach?

• -4(x - 1)

• 4(x - 1)

• -4(x + 1)

• 4(x + 1)

What happens to the expression (x + 1) in the denominator during the limit calculation?

• It remains unchanged.

• It becomes zero.

• It cancels out.

• It doubles.

What is the final value of the limit as x approaches -1?

• 11

• -4

• 4

• 0