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Algebra Parent Functions and Transformations

14 Questions

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Algebra Parent Functions and Transformations

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Questions and Answers

What is the parent function of a linear equation?

Y=x (correct)

Y=2^x

Y=x^2

Y=|x|

What is the parent function of a quadratic equation?

Y=|x|

Y=x^2 (correct)

Y=x

Y=2^x

What is the parent function of an exponential equation?

Y=2^x (correct)

Y=x^2

Y=|x|

Y=x

What is the parent function of absolute value?

Y=|x| Signup and view all the answers

The letter that is directly added or subtracted after x is?

H Signup and view all the answers

The letter that is added or subtracted to the end of the equation is?

K Signup and view all the answers

This number shifts up or down but the number stays the same?

K Signup and view all the answers

This number shifts left or right. The positive number goes left and the negative number goes right?

H Signup and view all the answers

M is what?

(Slope) rise over run Signup and view all the answers

What is the slope formula?

m=y2-y1/x2-x1 Signup and view all the answers

Parallel is?

Same slope Signup and view all the answers

Perpendicular is?

Negative reciprocals Signup and view all the answers

When solving parallel equations you must?

Use the same slope (m) but change the y intercept (b) Signup and view all the answers

When solving perpendicular equations you must?

Flip the slope (m) from negative to positive and choose a random number for the y intercept (b) Signup and view all the answers

Study Notes

Parent Functions

Linear equation parent function is defined as Y = x.
Quadratic equation parent function is represented by Y = x².
Exponential equation parent function is Y = 2^x.
Absolute value parent function is Y = |x|.

Transformations

The variable H represents horizontal shifts; a positive value shifts left, while a negative value shifts right.
The variable K indicates vertical shifts; it shifts the graph up or down without changing the shape.

Slope and Equations

M refers to slope, calculated as rise over run.
The slope formula is expressed as m = (y₂ - y₁) / (x₂ - x₁).
Parallel lines have the same slope, indicating they will never intersect.
Perpendicular lines have slopes that are negative reciprocals of each other.

Solving Equations

To solve parallel equations, maintain the same slope (m) but adjust the y-intercept (b).
When solving perpendicular equations, invert the slope (m) from negative to positive and select any number for the y-intercept (b).

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Description

This quiz covers the parent functions of various equations, including linear, quadratic, exponential, and absolute value functions. Additionally, it discusses transformations related to horizontal and vertical shifts, as well as the concepts of slope in equations and the characteristics of parallel and perpendicular lines.