Algebra 1: Translations and Reflections

Questions and Answers

What is the formula for a horizontal translation?

f(x-h) (correct)

f(x)+k

y=f(-x)

y=-f(x)

What is the formula for a vertical translation?

y=-f(x)

y=f(-x)

f(x-h)

f(x)+k (correct)

What is the reflection in the x-axis?

y=-f(x)

What is the reflection in the y-axis?

y=f(-x) Signup and view all the answers

What does a vertical stretch look like mathematically?

y=a*f(x) Signup and view all the answers

What is the formula for a horizontal stretch?

-y=f(ax) Signup and view all the answers

What is the formula for a horizontal shrink?

-y=f(ax) Signup and view all the answers

What are the zeros of a function?

Values of the variable for which the value of a function is zero. Signup and view all the answers

HOY indicates a horizontal line with a slope of 0, represented by y=______.

c Signup and view all the answers

VUX indicates a vertical line with an undefined slope, represented by x=____.

<h1></h1> Signup and view all the answers

What is the standard form of a linear equation?

Ax+By=C Signup and view all the answers

What is the slope-intercept form of a linear equation?

y=mx+b Signup and view all the answers

Study Notes

Translations

Horizontal translation represented as f(x-h), shifting the graph right or left by h units.
Vertical translation expressed as f(x) + k, moving the graph up or down by k units.

Reflections

Reflection in the x-axis defined as y = -f(x), creating a mirror image across the x-axis.
Reflection in the y-axis described as y = f(-x), creating a mirror image across the y-axis.

Stretches and Shrinks

Vertical stretch noted as y = a*f(x), where a is an integer greater than 1, elongating the graph vertically.
Vertical shrink represented as y = a*f(x), where a is a fraction, compressing the graph vertically.
Horizontal stretch indicated as -y = f(ax), where a is a fraction, expanding the graph horizontally.
Horizontal shrink shown as -y = f(ax), where a is an integer greater than 1, narrowing the graph horizontally.

Function Zeros and Characteristics

Zeros of a function are variable values where the function's output is zero, also known as function roots.

Special Lines

HOY means horizontal line with a slope of 0, described by the equation y = ____.
VUX signifies a vertical line with an undefined slope, expressed as x = #.

Forms of Equations

Standard form of a linear equation is given by Ax + By = C.
Slope-intercept form of a linear equation is represented as y = mx + b, where m is the slope and b is the y-intercept.

Description

Test your knowledge on horizontal and vertical translations, reflections, and stretches in Algebra 1. This quiz covers essential definitions and concepts that will help reinforce your understanding of transformations in functions.