Understanding Transformations of Functions

What happens to the x-intercept of a linear function when it is horizontally stretched?

• It becomes undefined.

• It moves farther from the y-axis.

• It remains unchanged.

• It moves closer to the y-axis.

In the context of quadratic equations, what does a difference in y-coordinates typically indicate?

• A change in the vertex.

• A horizontal scaling transformation.

• A vertical scaling transformation.

• No transformation.

How do you determine the 'a' value in the vertex form of a quadratic equation?

• By substituting x and y values from an ordered pair.

• By using the y-intercept.

• By finding the x-intercept.

• By calculating the slope.

What is the 'a' value for h(x) if the point (2,1) is used?

• 1/2

• 2

• 1

• 1/4

What does a horizontal stretch imply when transforming f(x) to h(x)?

• The x is multiplied by a number greater than 1.

• The x is multiplied by a number between 0 and 1.

• The entire function is multiplied by a number.

• The y-intercept changes.

What is the 'a' value for g(x) when using the point (1,4)?

• 1/4

• 1

• 2

• 4

What does a horizontal compress indicate in the transformation of f(x) to g(x)?

• The y-intercept changes.

• The x is multiplied by a number between 0 and 1.

• The x is multiplied by a number greater than 1.

• The entire function is multiplied by a number.

What is a common misunderstanding about f(kx) and kf(x)?

• They yield the same algebraic results.

• They yield the same graphical results.

• They are not related to scaling.

• They yield different results both algebraically and graphically.

What is the result of substituting 2 for k in f(kx) if f(x) = x^2 + 1?

• 4x^2 + 1

• x^2 + 2

• 4x^2 + 2

• 2x^2 + 2

What is the result of substituting 2 for k in kf(x) if f(x) = x^2 + 1?

• x^2 + 2

• 4x^2 + 1

• 2x^2 + 2

• 4x^2 + 2