Transformations in Algebra II

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Questions and Answers

If we replace every x in our function with x + 2, how will the graph change?

The graph will move to the left horizontally.

If we replace every x in our function with x - 2, how will the graph change?

The graph will move to the right horizontally.

If we multiply the entire function [f(x)] by 2, how will the graph change?

The graph will stretch vertically by a factor of 2.

If we multiply the entire function [f(x)] by 0.5, how will the graph change?

The graph will compress vertically by a factor of 2. Signup and view all the answers

If we replace every x in the function [f(bx)] with -x, how will the graph change?

The graph will translate over the y-axis. Signup and view all the answers

If we negate the entire function [f(x)], how will the graph change?

The graph will translate over the x-axis. Signup and view all the answers

If we replace every x in our function [f(bx)] with 2x, how will the graph change?

The graph will compress horizontally by a factor of 2. Signup and view all the answers

How do you know if a function is going to be dealing with horizontal or vertical changes?

Horizontal changes affect the x inside the equation [f(bx)] and vertical changes affect the x outside the equation (b)[f(x)]. Signup and view all the answers

How do you know if a function has an inverse?

If it can pass the horizontal line test, ensuring no x has more than one y. Signup and view all the answers

What is a function?

If it can pass the vertical line test, then it is a function. Signup and view all the answers

When an interval is increasing or decreasing, are the brackets open or closed?

Open. Signup and view all the answers

What coordinates do relative min/max have to do with?

Y-coordinates. Signup and view all the answers

If you have to stretch something vertically, what is a trick you can use?

Count how far away the y-coordinates are from the x-axis, and multiply by the vertical stretch number. Signup and view all the answers

What does vertical stretching & compression do?

Vertical stretching pulls away from the x-axis; vertical compression pulls towards the x-axis. Signup and view all the answers

What does horizontal stretching & compression do?

Horizontal stretching pulls away from the y-axis; horizontal compression pulls towards the y-axis. Signup and view all the answers

What is a compression?

A stretch by a factor less than one. Signup and view all the answers

Steps for finding the inverse of an equation without graphing.

<ol> <li>Flip the x and y. 2. Solve for y. 3. Rewrite with the new function name.</li> </ol> Signup and view all the answers

Steps for finding the inverse of an equation with graphing.

<ol> <li>Get one point from each graph. 2. Flip the x & y coordinates. 3. See if the coordinates fall on each other's graph.</li> </ol> Signup and view all the answers

If you have to compress something horizontally, what must you do?

Take the x-coordinates and multiply by the fraction given, keeping y-coordinates the same. Signup and view all the answers

If we replace every x in our function with 0.5, how will the graph change?

The graph will stretch horizontally. Signup and view all the answers

Study Notes

Transformations in Algebra II

Replacing every x with x+2 results in the graph moving left horizontally.
Replacing every x with x-2 results in the graph moving right horizontally.
Multiplying the entire function f(x) by 2 causes the graph to stretch vertically by a factor of 2.
Multiplying the entire function f(x) by 0.5 compresses the graph vertically by a factor of 2.
Replacing every x in the function with -x results in the graph translating over the y-axis.
Negating the entire function f(x) translates the graph over the x-axis.
Replacing every x in the function with 2x compresses the graph horizontally by a factor of 2.
Horizontal changes affect the x inside the equation f(bx), while vertical changes affect the x outside the equation b[f(x)].
A function has an inverse if it passes the horizontal line test, ensuring no x is paired with more than one y (one-to-one).
A relation is a function if it passes the vertical line test, ensuring no x has more than one y.
When an interval is increasing or decreasing, the brackets used to indicate the interval are typically open.
Relative min/max values are associated with y-coordinates of a function.
To stretch vertically, count the distance of y-coordinates from the x-axis and multiply by the vertical stretch factor.
Vertical stretching pulls points away from the x-axis, while vertical compression pulls points toward the x-axis.
Horizontal stretching pulls points away from the y-axis, and horizontal compression brings points toward the y-axis.
A compression is defined as a stretch by a factor less than one.
Steps to find the inverse of an equation without graphing:
- Flip x and y (where x becomes y).
- Solve for y.
- Rewrite the function with a new name.
Steps to find the inverse of an equation using graphing:
- Obtain one point from each graph.
- Flip the x and y coordinates.
- Check if the coordinates fall on each other's graphs.
To compress horizontally, multiply x-coordinates by the given fraction while keeping y-coordinates unchanged.
Replacing every x in the function with 0.5 results in the graph stretching horizontally.

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Description

This quiz covers the various transformations applied to functions in Algebra II, including shifts, stretches, and compressions. Understand how changing the equation affects the graph visually and how to determine inverses through the horizontal line test.