The video tutorial covers linear functions, focusing on how to identify and graph vertical and horizontal stretches and shrinks. It explains the transformations of linear functions by multiplying coordinates by a factor, affecting the graph's shape. The tutorial includes examples and practice exercises to reinforce understanding of these concepts.

What is the primary focus of the lesson on linear functions?

• Studying the integrals of polynomial functions

• Learning about the derivatives of functions

• Mastering vertical and horizontal transformations in linear functions

• Understanding quadratic functions

What happens to the y-intercept when a linear function undergoes a horizontal stretch?

• It changes based on the scale factor

• It remains unchanged

• It becomes zero

• It doubles in value

What is the scale factor for a horizontal stretch or shrink?

• The value of a

• One over a

• The square of a

• Two times a

During a vertical stretch, if the factor a is greater than one, what happens to the graph?

• It moves closer to the y-axis

• It shrinks towards the x-axis

• It stretches away from the x-axis

• No change occurs

What remains the same when a linear function is vertically stretched or shrunk?

• Neither intercept

• Both intercepts

• The x-intercept

• The y-intercept

How do you describe the transformation from function f to function g if g(x) = 1/2 f(x)?

• Horizontal shrink by a factor of 2

• Horizontal stretch by a factor of 2

• Vertical stretch by a factor of 2

• Vertical shrink by a factor of 2

What is the correct slope-intercept form of function g if it is a transformation of function f by replacing x with 1/2x?

• g(x) = 2x + 3

• g(x) = x/2 + 3

• g(x) = 3x + 1/2

• g(x) = x + 1.5

If a vertical stretch has a factor a greater than one, what can be said about the x-intercept?

• It is halved

• It becomes zero

• It doubles

• It remains the same

What transformation occurs if the function g is obtained by multiplying function f by 3?

• Vertical stretch by a factor of 3

• Horizontal shrink by a factor of 3

• Vertical shrink by a factor of 3

• Horizontal stretch by a factor of 3

In the context of linear transformations, what does a scale factor of 1/4 indicate?

• Horizontal stretch by a factor of 4

• Vertical stretch by a factor of 4

• Horizontal shrink by a factor of 4

• Vertical shrink by a factor of 4