Question

Determine whether the points (a) $(3,2),$ (b) $(1,1),$ and $(\mathrm{c})$ (-5,2) lie on the graph of $f(x)=\sqrt{x+1},$ without referring to a picture of the graph of $f$.

Name: Problem 7, Chapter 0: Calculus
Uploaded: 2022-02-06T00:55:04-08:00
Duration: 1 min 16 s
Channel: Raj Bala
Description: Determine whether the points (a) (3,2), (b) (1,1), and (c) (-5,2) lie on the graph of f(x)=√(x+1), without referring to a picture of the graph of f.

   Determine whether the points (a) $(3,2),$ (b) $(1,1),$ and $(\mathrm{c})$ (-5,2) lie on the graph of $f(x)=\sqrt{x+1},$ without referring to a picture of the graph of $f$.

Calculus

Laura Taalman, Peter… 1st Edition

Chapter 0, Problem 7

Instant Answer

Solved by Expert Raj Bala

02/06/2022

Step 1

Step 1: First, we need to substitute the x-values of the given points into the function $f(x)=\sqrt{x+1}$ and see if the resulting y-values match the y-values of the given points. Show more…

Show all steps

Thanks for your feedback!

Determine whether the points (a) $(3,2),$ (b) $(1,1),$ and $(\mathrm{c})$ (-5,2) lie on the graph of $f(x)=\sqrt{x+1},$ without referring to a picture of the graph of $f$.

Play audio

Feedback

Raj Bala and 91 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Function Evaluation

This concept involves substituting a given input into the function's formula to verify if the resulting output equals the corresponding coordinate's y-value. It is a fundamental method for determining if a point lies on the graph of the function.

Domain Considerations

Functions have domains that represent the set of all allowable inputs. For functions involving square roots, the expression inside must be non-negative, making it essential to check that a tested x-value falls within this allowed set before evaluating the function.

Properties of Square Root Functions

Square root functions are defined to return only non-negative outputs and are limited to inputs that make the radicand non-negative. Understanding these inherent restrictions is key when determining the validity of points on their graphs.

Please give Ace some feedback