Transformation and Function

¡Supera tus tareas y exámenes ahora con Quizwiz!

When multiple translations are applied to a function, in what order are the translations done in?

SRT: stretches, reflections, transformations.

What is the inverse function of y=f(x)?

y=f(-1 an exponent)(x)

Invariant Point

Point on a graph that remains unchanged after a transformation is applied to it, any point on a curve that lies on a line of reflection.

Reflection

Transformation where each point of original graph has an image point resulting from a reflection in a line; may result in a change of orientation of a graph while preserving its shape.

Relating to stretches what would the equation y= af(x) do to a graph?

When y= af(x) is multiplied by a, the result is a vertical stretch about the x-axis by a factor of |a|. If a is < 0 the graph is also reflected in the x-axis.

Relating to stretches what would the equation y= f(bx) do to a graph?

When y= f(bx)is multiplied by b, a horizontal stretch occurs about the y-axis by a factor of 1/|b|. If b < 0 the graph is also reflected about the y-axis.

Relating to reflections what would the equations y= -f(x) and y= f(-x) do to a graph?

Y= -f(x) would be a vertical reflection over the x-axis and (x.y) would become (x, -y) Y= f(-x) would be a horizontal reflection over the y-axis and (x,y) would become (-x,y).

In the equaution y=f(x-h), what happens to a graph if h is positive vs. when h is negative?

If h is negative (y=f(x-4)) then a horizontal translation 4 units right occurs, if h is positive (y=f(x+4)) then a horizontal translation 4 units left occurs.

In the equation y-k=f(x), what happens to a graph if k is positive vs. when k is negative?

If k is positive (y=f(x)+4) then a vertical translation 4 units up occurs, if k is negative (y=f(x)-4) then a vertical translation 4 units down occurs.

What are the three ways to determine the inverse of a function?

Interchange x and y values: 1. (x,y) --> (y,x) 2. y= f(x) --> x= f(y) 3. Reflect in the line y=x

In the equation y= af[b(x-h)] + k what do all of the variables do in relation to a function?

In this equation, a: is a vertical stretch by factor a and if a < 0 a reflection about the x-axis also occurs, b is a horizontal stretch by the factor of 1/b and if b < 0 than a reflection about the y-axis occurs. H is a horizontal translation and k is a vertical translation.

Stretch

Transformation where the distance of each x or y coordinate from the line of reflection is multiplied by a scale factor; scale factors between 0 and 1 result in the point moving closer to the line of reflection and a scale factor greater than 1 results in the point moving farther away from the line of reflection.


Conjuntos de estudio relacionados

SAP ABAP Specialist for HANA 2.0 Exam questions

View Set

Black Psychology (Phia Salter) Ch. 1 People

View Set

AICPA Ch.1-5 Questions - Financial Accounting

View Set

Systems Analysis & Design: CH 9 MC Questions

View Set

S294: Book 2: Chapter 2: Cell membranes

View Set

Physical Assistance and Monitoring Medical Emergencies

View Set