Transformations of Linear Function Graphs

The video tutorial covers graphing linear equations and transformations, focusing on parent functions and their transformations. It explains the concept of a family of functions, introduces translation and reflection transformations, and provides examples of graphing these transformations. The tutorial emphasizes understanding how transformations affect the position, size, and orientation of graphs.

What is the simplest form of a linear function in this context?

• y = mx + b

• y = x

• y = mx

• x = y

In the context of graph transformations, what does the term 'parent function' refer to?

• The function derived from another function

• The simplest function in a family

• The function with the highest degree

• The most complex function in a family

What is a family of functions?

• A series of functions with varying intercepts

• A group of functions with similar characteristics

• A collection of graphs with different characteristics

• A set of unrelated mathematical equations

What does a horizontal translation involve?

• Stretching the graph horizontally

• Moving the graph left or right

• Rotating the graph around the origin

• Shifting the graph up or down

If a function is translated vertically up, what is the mathematical representation?

• f(x) - k

• f(x + k)

• f(x - k)

• f(x) + k

What indicates a horizontal shift to the left in a function's equation?

• Multiplying x by a negative number

• Adding a number to x in the function

• Subtracting a number from x in the function

• Dividing x by a negative number

Which transformation does not change the size or shape of the graph?

• Translation

• Dilation

• Rotation

• Reflection

What does reflecting a graph across the x-axis alter?

• The shape of the graph

• The vertical position

• The horizontal position

• The orientation vertically

How is a reflection across the y-axis represented if the function is f(x)?

• f(-x)

• -f(x)

• f(x) + 1

• -f(x + 1)

What transformation is applied if the function changes from f(x) to f(x) - 3?

• Horizontal compression

• Vertical shift downwards

• Horizontal shift to the right

• Vertical stretch