The function of the graph is [tex]\boxed{y = {{\log }_3}x}[/tex]. Option (c) is correct.
Further explanation:
The properties of the logarithm are as follows,
1. [tex]{\log _a}a = 1[/tex]
2. [tex]{\log _a}1 = 0[/tex]
Given:
The options of the equations are as follows.
1. [tex]y = {\log _{0.4}}x[/tex]
2. [tex]y = {\log _{1}}x[/tex]
3. [tex]y = {\log _{3}}x[/tex]
4. [tex]y = {\log _{10}}x[/tex]
Explanation:
Consider the equation [tex]y = {\log _3}\left( x \right).[/tex]
The points on the curve are [tex]\left( {1,0} \right)[/tex] and [tex]\left( {3,1} \right).[/tex]
The points lie on the curve. Therefore, it satisfies the equation.
Substitute 1 for x in equation [tex]y = {\log _3}\left( x \right)[/tex] to check whether the point lies on the graph.
[tex]\begin{aligned}y&= {\log _3}\left( 1 \right)\\y&= 0\\\end{aligned}[/tex]
The point [tex]\left( {1,0} \right)[/tex] satisfies the equation.
Substitute [tex]3[/tex] for [tex]x[/tex] in equation [tex]y = {\log _3}\left( x \right)[/tex] to check whether the point lies on the graph.
[tex]\begin{aligned}y&= {\log _3}\left( 3 \right) \\y&= 1\\\end{aligned}[/tex]
The point [tex]\left( {3,1} \right)[/tex] satisfies the equation.
Hence, the function of the graph is [tex]\boxed{y = {{\log }_3}x}[/tex]. Option (c) is correct.
Option (a) is not correct.
Option (b) is not correct.
Option (c) is correct.
Option (d) is not correct.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: polynomials
Keywords: quadratic equation, equation factorization, polynomial, quadratic formula, zeroes, function.
