Graphing and Analyzing Functions

The video tutorial explains how to find limits graphically using a piecewise function G(x). The function is defined as x^2 + 1 for x < 0 and 2x + 3 for x >= 0. The tutorial demonstrates graphing these functions and finding the limit of G(x) as x approaches -2, which is determined to be 5. It also discusses the limit as x approaches zero, concluding that it does not exist due to differing values from the left and right.

What is the purpose of finding limits graphically?

• To understand the behavior of a function as it approaches a certain point

• To solve algebraic equations

• To determine the exact value of a function at a point

• To find the derivative of a function

What type of function is G(x) described as?

• Linear function

• Quadratic function

• Piecewise function

• Exponential function

What is the expression for G(x) when x is less than 0?

• 3x^2

• x - 1

• x^2 + 1

• 2x + 3

What shape does the graph of x^2 + 1 take?

• A straight line

• A parabola

• A circle

• A hyperbola

For which x-values is the function x^2 + 1 defined?

• x >= 0

• x < 0

• x > 0

• x <= 0

What is the y-intercept of the line 2x + 3?

• 4

• 1

• 3

• 2

What is the slope of the line 2x + 3?

• 3

• 2

• 0

• 1

What does the graph of 2x + 3 look like?

• A vertical line

• A horizontal line

• A parabola

• A slanted line

What is the limit of G(x) as x approaches -2?

• 6

• 4

• 3

• 5

What happens to the y-values as x gets closer to -2?

• They approach 0

• They approach 3

• They approach 5

• They approach -2