All Algebra II Resources
Example Questions
Example Question #41 : Transformations Of Linear Functions
Shift the graph three units to the left. What's the new equation?
In order to shift an equation to the left three units, the x-variable will need to be replaced with the quantity of . This shifts all points left three units.
Simplify the equation.
The answer is:
Example Question #42 : Transformations Of Linear Functions
Shift the line up six units. What is the new equation?
Add six to the equation since a vertical shift will increase the y-intercept by six units.
Simplify this equation by distribution.
The answer is:
Example Question #43 : Transformations Of Linear Functions
Translate the function: to the left 5 units. What is the equation in slope-intercept format?
Divide by three on both sides.
The equation becomes:
If this equation shifts to the left five units, we will need to replace the x term with the quantity .
Simplify this equation by distribution.
Combine like-terms.
The answer is:
Example Question #44 : Transformations Of Linear Functions
Translate the function to the left four units. What is the new equation?
Translation of a graph to the left four units will require replacing the x-variable with the quantity:
Replace the term inside the equation.
Use distribution so simplify the terms.
Simplify the equation.
The answer is:
Example Question #45 : Transformations Of Linear Functions
Shift the equation up two units. What is the new equation?
In order to find the equation after the translation, we will need to put the equation in slope-intercept format, .
Subtract from both sides of the equation.
The equation becomes:
Divide by three on both sides.
Add two to the y-intercept for the vertical shift. This is the same as adding .
The equation is:
Example Question #46 : Transformations Of Linear Functions
If the graph is translated 5 units left, what is the new equation?
Rewrite the given equation in standard form to slope intercept format, .
Subtract x from both sides.
The slope intercept form is:
If the line is translated 5 units to the left, we need to replace the quantity of x with .
Simplify the equation. Distribute the negative through the binomial.
The answer is:
Example Question #47 : Transformations Of Linear Functions
Shift the graph down four units. What is the new equation?
Rewrite this equation in slope intercept form .
Add on both sides.
The equation becomes:
Divide by two on both sides.
The equation in slope intercept form is:
Shifting this equation down four units means that the y-intercept will be decreased four units.
The answer is:
Example Question #48 : Transformations Of Linear Functions
Shift the line left three units. What is the new equation?
Rewrite the equation in slope-intercept form:
Subtract one from both sides.
Divide by three on both sides.
If this line is shifted to the left three units, replace the x-variable with .
Simplify by distribution.
The answer is:
Example Question #49 : Transformations Of Linear Functions
Shift the equation to the left two units. What is the new equation?
If the linear function is shifted left two units, the x-variable must be replaced with the quantity of .
Simplify the equation by distribution.
Combine like terms.
The answer is:
Example Question #51 : Transformations Of Linear Functions
Translate the equation left four units. What is the new equation?
To shift the line left four units, we will need to replace the x-variable with the quantity of:
Replace this term in the original equation.
Use distribution to simplify.
The answer is: