Question

Which function is shown in the graph below?

Answer 1

Set up the equations to solve for X >0 since the curve goes up to the right
 doing that proves that y=log3(x)

the answer is C


 see attached picture:

Answer 2

The function of the graph is $\boxed{y = {{\log }_3}x}$. Option (c) is correct.

Further explanation:

The properties of the logarithm are as follows,

1. ${\log _a}a = 1$

2. ${\log _a}1 = 0$

Given:

The options of the equations are as follows.

1. $y = {\log _{0.4}}x$

2. $y = {\log _{1}}x$

3. $y = {\log _{3}}x$

4. $y = {\log _{10}}x$

Explanation:

Consider the equation $y = {\log _3}\left( x \right).$

The points on the curve are $\left( {1,0} \right)$ and $\left( {3,1} \right).$

The points lie on the curve. Therefore, it satisfies the equation.

Substitute 1 for x in equation $y = {\log _3}\left( x \right)$ to check whether the point lies on the graph.

$\begin{aligned}y&= {\log _3}\left( 1 \right)\\y&= 0\\\end{aligned}$

The point $\left( {1,0} \right)$ satisfies the equation.

Substitute $3$ for $x$ in equation $y = {\log _3}\left( x \right)$ to check whether the point lies on the graph.

$\begin{aligned}y&= {\log _3}\left( 3 \right) \\y&= 1\\\end{aligned}$

The point $\left( {3,1} \right)$ satisfies the equation.

Hence, the function of the graph is $\boxed{y = {{\log }_3}x}$. 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 brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: polynomials

Keywords: quadratic equation, equation factorization, polynomial, quadratic formula, zeroes, function.