Algebra 2 Parent Functions & Transformations

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Questions and Answers

What does the term 'family of graphs' refer to?

  • Graphs only for linear equations
  • A single graph type
  • Graphs that display similar characteristics (correct)
  • Graphs without any characteristics

What is a parent function?

The simplest function of the family

What is the linear equation expressed mathematically?

f(x)=x

What is the linear domain?

<p>All real numbers</p> Signup and view all the answers

What is the linear x-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the linear range?

<p>All real numbers</p> Signup and view all the answers

What is the linear y-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the maximum number of roots/zeros for a linear function?

<p>1</p> Signup and view all the answers

What does end behavior of a function describe?

<p>How the line continues towards negative or positive infinity</p> Signup and view all the answers

What is the end behavior of a linear function?

<p>As x goes to -infinity, f(x) goes to -infinity; as x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

Is a linear function continuous or discontinuous?

<p>Continuous</p> Signup and view all the answers

What is the absolute value equation mathematically expressed?

<p>f(x)=|x|</p> Signup and view all the answers

What is the absolute value domain?

<p>All real numbers</p> Signup and view all the answers

What is the absolute value range?

<p>y is greater than or equal to 0</p> Signup and view all the answers

What is the absolute value x-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the absolute value y-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the maximum number of roots/zeros for an absolute value function?

<p>2</p> Signup and view all the answers

Is the absolute value function continuous or discontinuous?

<p>Continuous</p> Signup and view all the answers

What is the end behavior of an absolute value function?

<p>If x goes to -infinity, f(x) goes to infinity; if x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

What is the quadratic equation expressed mathematically?

<p>f(x)=x squared</p> Signup and view all the answers

What is the quadratic domain?

<p>All real numbers</p> Signup and view all the answers

What is the quadratic range?

<p>y is greater than or equal to 0</p> Signup and view all the answers

What is the quadratic x-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the quadratic y-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the maximum number of roots/zeros for a quadratic function?

<p>2</p> Signup and view all the answers

What is the end behavior of a quadratic function?

<p>If x goes to -infinity, f(x) goes to infinity; if x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

Is the quadratic function continuous or discontinuous?

<p>Continuous</p> Signup and view all the answers

What is the cubic equation in mathematical terms?

<p>f(x)=x cubed</p> Signup and view all the answers

What is the cubic domain?

<p>All real numbers</p> Signup and view all the answers

What is the cubic range?

<p>All real numbers</p> Signup and view all the answers

What is the cubic x-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the cubic y-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the maximum number of roots/zeros for a cubic function?

<p>3</p> Signup and view all the answers

What is the end behavior of a cubic function?

<p>If x goes to -infinity, f(x) goes to -infinity; If x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

Is the cubic function continuous or discontinuous?

<p>Continuous</p> Signup and view all the answers

What are asymptotes?

<p>A curve that gets closer and closer to 0 but never touches it</p> Signup and view all the answers

What is the square root equation expressed mathematically?

<p>f(x)= square root of x</p> Signup and view all the answers

What is the square root domain?

<p>x is greater than or equal to zero</p> Signup and view all the answers

What is the square root range?

<p>y is greater than or equal to zero</p> Signup and view all the answers

What is the square root x-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the square root y-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the maximum number of roots/zeros for a square root function?

<p>1</p> Signup and view all the answers

What is the end behavior of a square root function?

<p>As x goes to 0, f(x) goes to 0; as x goes to infinity, f(x) goes to infinity.</p> Signup and view all the answers

Is the square root function continuous or discontinuous?

<p>Discontinuous</p> Signup and view all the answers

What is the cube root equation expressed mathematically?

<p>f(x)= cube root of x</p> Signup and view all the answers

What is the cube root domain?

<p>All real numbers</p> Signup and view all the answers

What is the cube root range?

<p>All real numbers</p> Signup and view all the answers

What is the cube root x-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the cube root y-intercept?

<p>(0,0)</p> Signup and view all the answers

What is the maximum number of roots/zeros for a cube root function?

<p>1</p> Signup and view all the answers

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Study Notes

Graph Families and Parent Functions

  • Family of graphs share similar characteristics and display distinct forms.
  • Parent function is the simplest representation within a graph family.

Linear Functions

  • Linear equation defined as f(x) = x.
  • Domain includes all real numbers.
  • X-intercept and Y-intercept both at (0,0).
  • Range also consists of all real numbers.
  • Maximum number of roots/zeros for linear functions is 1.
  • End behavior: As x approaches -∞, f(x) approaches -∞; as x approaches ∞, f(x) approaches ∞.
  • Linear functions are continuous without breaks.

Absolute Value Functions

  • Absolute value equation as f(x) = |x|.
  • Domain includes all real numbers.
  • Range includes values where y is greater than or equal to 0.
  • X-intercept and Y-intercept both at (0,0).
  • Maximum number of roots/zeros for absolute value functions is 2.
  • End behavior: As x approaches -∞, f(x) approaches ∞; as x approaches ∞, f(x) also approaches ∞.
  • Absolute value functions are continuous.

Quadratic Functions

  • Quadratic equation expressed as f(x) = x².
  • Domain includes all real numbers.
  • Range includes values where y is greater than or equal to 0.
  • X-intercept and Y-intercept both at (0,0).
  • Maximum number of roots/zeros for quadratic functions is 2.
  • End behavior: As x approaches -∞, f(x) approaches ∞; as x approaches ∞, f(x) also approaches ∞.
  • Quadratic functions are continuous.

Cubic Functions

  • Cubic equation is f(x) = x³.
  • Domain includes all real numbers.
  • Range also includes all real numbers.
  • X-intercept and Y-intercept both at (0,0).
  • Maximum number of roots/zeros for cubic functions is 3.
  • End behavior: As x approaches -∞, f(x) approaches -∞; as x approaches ∞, f(x) approaches ∞.
  • Cubic functions are continuous.

Square Root Functions

  • Square root equation as f(x) = √x.
  • Domain requires x to be greater than or equal to 0.
  • Range includes values where y is greater than or equal to 0.
  • X-intercept and Y-intercept both at (0,0).
  • Maximum number of roots/zeros for square root functions is 1.
  • End behavior: As x approaches 0, f(x) approaches 0; as x approaches ∞, f(x) approaches ∞.
  • Square root functions are discontinuous.

Cube Root Functions

  • Cube root equation expressed as f(x) = ∛x.
  • Domain includes all real numbers.
  • Range also includes all real numbers.
  • X-intercept and Y-intercept both at (0,0).
  • Maximum number of roots/zeros is 1.
  • End behavior similar to cubic functions, with f(x) approaching -∞ as x goes to -∞ and ∞ as x goes to ∞.
  • Cube root functions are continuous.

Asymptotes

  • Describes curves that approach a line or value but never touch it.

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