Exploring Transformations of Linear Functions

What is a transformation in the context of linear functions?

• A way to find the slope of a line.

• A method to solve linear equations.

• A change in the size, shape, position, or orientation of a graph.

• A technique to calculate the y-intercept.

What is the parent function for linear functions?

• f(x) = x^2

• f(x) = 1/x

• f(x) = |x|

• f(x) = x

In a horizontal translation, if the equation is y = f(x + h), which direction does the graph shift?

• Left

• Right

• Up

• Down

In a vertical translation, if the equation is y = f(x) - k, which direction does the graph shift?

• Up

• Down

• Right

• Left

What does a reflection over the x-axis do to the graph of a function?

• Shifts it up

• Shifts it down

• Flips it over the y-axis

• Flips it over the x-axis

If a function is reflected over the y-axis, which part of the function is made opposite?

• The y-intercept

• The y-values

• The x-values

• The slope

In a horizontal stretch, if the factor is 1/2, what happens to the graph?

• It stretches by a factor of 1/2

• It stretches by a factor of 2

• It shrinks by a factor of 1/2

• It shrinks by a factor of 2

In a vertical stretch, if the factor is 3, what happens to the graph?

• It stretches by a factor of 1/3

• It shrinks by a factor of 1/3

• It shrinks by a factor of 3

• It stretches by a factor of 3

What is the first step when combining multiple transformations?

• Translate horizontally

• Translate vertically

• Reflect

• Stretch or shrink

In the example of combining transformations, what is the final transformation applied?

• Stretch or shrink

• Reflect

• Translate horizontally

• Translate vertically