Recognizing and Graphing Stretches and Shrinks of Linear Functions

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