Graphing Functions Flashcards
24 Questions
102 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the Graph of a quadratic function?

What is the Graph of an absolute value function?

What is the graph of a linear function?

What is a linear function?

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

What is the Graph of a cube root function?

Signup and view all the answers

What is transformation/translation in graphing?

<p>A change in the size, shape, position or orientation of a graph.</p> Signup and view all the answers

What is a parent function?

<p>The most basic function in a family of functions.</p> Signup and view all the answers

What is the equation of a quadratic function?

<p>f(x) = a(x-h)^2 + k, where 'a' does not equal zero.</p> Signup and view all the answers

What is an absolute value function?

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

What is the Graph of a square root function?

Signup and view all the answers

What is domain in the context of functions?

<p>Possible x-values for a given function.</p> Signup and view all the answers

What is range in the context of functions?

<p>Possible y-values for a given function.</p> Signup and view all the answers

What is the Graph of a cubic equation?

Signup and view all the answers

What is a function with a shift left of 1?

<p>f(x + 1)</p> Signup and view all the answers

What is a function with a shift up of 1?

<p>f(x) + 1</p> Signup and view all the answers

What is a function with a shift right of 1?

<p>f(x - 1)</p> Signup and view all the answers

What does 'All Real Numbers' represent?

<p>The domain of all quadratic functions.</p> Signup and view all the answers

What is a relation in mathematics?

<p>A set of ordered pairs.</p> Signup and view all the answers

What is a function?

<p>A set of ordered pairs in which the x-values do not repeat.</p> Signup and view all the answers

What does 'distribute' refer to in solving equations?

<p>It is the first step in solving $2(x + 3) = 9$.</p> Signup and view all the answers

What is the simplified form of: -x > 2?

<p>x &lt; -2</p> Signup and view all the answers

What is an exponential function?

Signup and view all the answers

What is a logarithmic function?

Signup and view all the answers

What relationship do inverses have to exponential and logarithmic functions?

<p>They are inverses of each other.</p> Signup and view all the answers

Study Notes

Graph of Functions

  • Quadratic functions have a parabolic shape, opening either upwards or downwards based on the coefficient of the squared term.
  • Absolute value functions produce a V-shaped graph, reflecting all negative values upwards to positive.
  • Linear functions create straight lines, represented by the equation f(x) = mx + b where m is the slope and b is the y-intercept.
  • The cube root function has an S-shaped graph that extends in all four quadrants, allowing for both positive and negative outputs.

Types of Functions

  • Linear function is defined as f(x) = x, representing a line with a slope of 1.
  • Absolute value function can be expressed as f(x) = | x |, which outputs the distance of x from zero, always yielding non-negative results.
  • Quadratic functions can be represented in vertex form as f(x) = a(x-h)² + k, where "a" determines the direction and width of the parabola.
  • The square root function graphs as a half-parabola only in the positive x-region.
  • The domain of any function specifies the possible x-values, while the range determines the possible y-values.

Transformations and Relations

  • Transformations refer to modifications in size, shape, position, or orientation of a graph.
  • A parent function is the simplest form of a function in its category, serving as the basis for all transformations.
  • A function with a left shift of 1 is represented as f(x + 1); shifting right is f(x - 1); and upward shift is denoted by f(x) + 1.
  • The domain for all quadratic functions includes all real numbers, allowing for any x-value input.
  • A relation is any set of ordered pairs, while a function is a relation where no x-values repeat.

Additional Concepts

  • The distributive property is often the first step in simplifying expressions, such as in 2(x + 3) = 9.
  • The solution for the inequality - x > 2 simplifies to x < -2.
  • Exponential functions grow rapidly and can be expressed in the form f(x) = a(b^x), where a is a constant and b is the base.
  • Logarithmic functions are the inverse of exponential functions and can be represented as y = log_b(x), where b is the base.
  • Exponential and logarithmic functions are inversely related, meaning they can undo each other's operations.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Description

Test your knowledge of various graphs with these flashcards focused on quadratic, absolute value, linear, and cube root functions. Each card presents a definition to deepen your understanding of graph transformations and translations. Perfect for students learning about graphing functions in mathematics.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser