Tangent Lines and Function Transformations

The video tutorial covers the concepts of tangents and normals in mathematics, focusing on how to find the equation of a tangent line using a given point and gradient. It also explains the properties of normals, including the concept of perpendicularity and negative reciprocals. The lesson includes a graphical representation of functions and transformations, using tools like Desmos to visualize these concepts. The tutorial concludes with a discussion on horizontal reflections and their effects on functions.

What platform is mentioned for accessing additional work?

• Google Classroom

• Moodle

• Blackboard

• Canvas

What two pieces of information are needed to find the equation of a tangent line?

• Point and gradient

• Point and angle

• Gradient and length

• Length and angle

Which mathematical concept helps in determining the gradient of a tangent?

• Limit

• Derivative

• Matrix

• Integral

What is the gradient of the normal line if the tangent's gradient is 8?

• 8

• 1/8

• -1/8

• -8

What is the relationship between the gradients of perpendicular lines?

• They are additive inverses

• They are multiplicative inverses

• They are negative reciprocals

• They are equal

Which tool is used to visualize the function and its tangents and normals?

• Desmos

• GeoGebra

• Wolfram Alpha

• Mathematica

What is the effect of subtracting 2 from x in the function f(x)?

• Shifts the graph right by 2 units

• Shifts the graph left by 2 units

• Shifts the graph down by 2 units

• Shifts the graph up by 2 units

What is the equation of the tangent line derived in the video?

• y - 4 = 1/8(x - 2)

• y - 4 = -8(x - 2)

• y - 4 = 8(x - 2)

• y - 4 = -1/8(x - 2)

What is the equation of the normal line derived in the video?

• y - 4 = -1/8(x - 2)

• y - 4 = 1/8(x - 2)

• y - 4 = -8(x - 2)

• y - 4 = 8(x - 2)

What happens to a function when it undergoes a horizontal reflection?

• It shifts down

• It shifts up

• It flips over the y-axis

• It flips over the x-axis