Graphing and Analyzing Functions

The video tutorial covers various mathematical graphs, including parabolas, cubic curves, linear functions, and hyperbolas. It explains the properties of each graph, such as vertices, intercepts, gradients, and asymptotes. The tutorial emphasizes the importance of understanding graph scales and how to determine specific points on a graph by substituting values into equations. It also highlights the need for arrows on graphs to indicate continuity and the significance of drawing graphs to scale for accurate representation.

What is the shape of a graph that starts with a 'p' and has a smooth curve?

• Hyperbola

• Linear Function

• Cubic Curve

• Parabola

If x = 1 in a parabola's equation, what is the y-value when the equation is y = -x²?

• 1

• -1

• 0

• 2

How do you find the x-intercept of a cubic curve?

• Set y to zero

• Find the vertex

• Use the gradient

• Set x to zero

What is the x-intercept of the cubic curve given by the equation y = x³ + 1?

• 1

• -1

• 0

• 2

What does a gradient of 1/2 indicate about a linear function?

• Steep slope

• No slope

• Shallow slope

• Negative slope

What is the y-intercept of a linear function with the equation y = 1/2x + 2?

• 0

• 3

• 2

• 1

Why is it important to draw graphs to scale?

• To ensure all intercepts are visible

• To avoid using a ruler

• To use less paper

• To make them look nice

What are the dotted lines on a hyperbola called?

• Axes

• Vertices

• Intercepts

• Asymptotes

Why does a hyperbola never collide with the axes?

• It has asymptotes

• It is a closed shape

• It is a straight line

• It is a parabola

What is a simple x-value to use when determining a point on a hyperbola?

• 2

• 3

• 0

• 1