Understanding Function Transformations

The video tutorial covers the concept of transformations in mathematics, focusing on translasi (translation) and dilatasi (dilation). It explains how these transformations affect functions by altering their input and output through addition, subtraction, multiplication, or division by constants. The tutorial provides examples of translasi in linear and quadratic functions, demonstrating how these transformations shift graphs horizontally and vertically. The video also touches on related geometric transformations like reflection and rotation, providing a comprehensive understanding of how transformations are applied in various mathematical contexts.

What does the term 'transformation' in functions generally refer to?

• Changing the shape of a graph

• Altering the constants in a function

• Modifying the input and output values

• Switching the variables in a function

Which of the following is NOT a type of transformation discussed in the video?

• Translation

• Reflection

• Inversion

• Rotation

In function transformations, what does a 'translation' specifically involve?

• Rotating the graph around a point

• Scaling the graph larger or smaller

• Shifting the graph horizontally or vertically

• Changing the slope of a line

Which transformation involves changing the size of a function's graph?

• Translation

• Dilation

• Reflection

• Rotation

What is the result of translating the function f(x) = 2x - 3 upwards by 3 units?

• f(x) = 2x

• f(x) = 2x + 3

• f(x) = 2x + 6

• f(x) = 2x - 6

When a function is translated to the left by 4 units, what happens to its graph?

• It moves to the left

• It moves to the right

• It moves down

• It moves up

How is a translation factor typically represented in mathematical terms?

• As a polynomial

• As a matrix

• As a pair of coordinates

• As a single number

What is the new function after translating f(x) = x^2 + 2x + 1 to the right by 2 units?

• f(x) = x^2 - 2x + 1

• f(x) = x^2 + 2x - 1

• f(x) = (x + 2)^2 + 2(x + 2) + 1

• f(x) = (x - 2)^2 + 2(x - 2) + 1

How do you determine the axis of symmetry for a translated quadratic function?

• By identifying the y-intercept

• By finding the vertex

• By using the formula x = -b/2a

• By calculating the midpoint

What is the axis of symmetry for the function f(x) = x^2 - 2x + 1?

• x = 2

• x = -1

• x = 0

• x = 1