Parent Functions Overview

Questions and Answers

What is the equation of the Linear Parent Function?

y = ax + b

y = √x

y = x (correct)

y = x^2

What is the simplest parabola represented by the Quadratic Parent Function?

y = x^2

The Absolute Value Function contains an algebraic expression without absolute value symbols.

False

Where do you start graphing the Cubic Parent Function?

(0, 0) Signup and view all the answers

What type of function is the Logarithmic Parent Function the inverse of?

Exponential Function Signup and view all the answers

What is the function notation for the Rational Parent Function?

f(x) = 1/x Signup and view all the answers

Exponential functions have the form y = _____

ab^x Signup and view all the answers

What is the parent function for functions of the form f(x) = √x - a + b?

f(x) = √x Signup and view all the answers

Study Notes

Linear Parent Function

Defined by the equation y = x with a constant slope.
Domain and range include all real numbers.

Quadratic Parent Function

Simplest form is y = x^2, resulting in a parabola.
Graph passes through the origin (0,0).
Situated primarily in Quadrants I and II.

Absolute Value Function

Features algebraic expressions enclosed within absolute value symbols.
Outputs only non-negative values regardless of the input.

Cubic Parent Function

Expressed as f(x) = x^3, starting at the origin (0, 0).
Characterizes a curve that extends into all four quadrants.

Logarithmic Parent Function

Functions such as y = loga x or y = ln x act as inverses to exponential functions.
Essential for solving equations involving exponentials.

Rational Parent Function

Defined by f(x) = 1/x, resulting in a hyperbola.
Domain and range exclude the value 0, as it causes the function to be undefined.
Excluded values represent x-values that make f(x) undefined.

Exponential Parent Function

Formulated as y = ab^x where a and b are positive, and b ≠ 1.
Represents growth or decay processes, fundamental in various scientific disciplines.

Square Root Function

Parent function is defined as f(x) = √x, which yields non-negative outputs.
Graph starts at the origin (0,0) and opens to the right.

Description

This quiz covers various parent functions including linear, quadratic, absolute value, cubic, logarithmic, and rational functions. It explores their definitions, characteristics, and graphs. Test your understanding of these foundational mathematical concepts.