[tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph.
How to find a function based on a graph
According to the statement, we must find a function such that all values of [tex]x[/tex] so that [tex]y(x) = 0[/tex] and are the same of the graph. A quick approach consists in solving on each expression:
Expression A
[tex]\log_{3}x-1 = 0[/tex]
[tex]\log_{3}x = 1[/tex]
[tex]x = 3[/tex]
Expression B
[tex]3\cdot x - 3 = 0[/tex]
[tex]3\cdot x = 3[/tex]
[tex]x = 1[/tex]
Expression C
[tex]-3\cdot (x-1) + 3 = 0[/tex]
[tex]-3\cdot x +6 = 0[/tex]
[tex]x = 2[/tex]
Expression D
[tex]\log_{3}2x - 2 = 0[/tex]
[tex]\log_{3}2x = 2[/tex]
[tex]2\cdot x = 9[/tex]
[tex]x = \frac{9}{2}[/tex]
Hence, we conclude that [tex]y = \log_{3}x - 1[/tex] is the equation with real zeros corresponding to the x-intercepts of the graph. [tex]\blacksquare[/tex]
Remarks
The graph is missing and all functions are poorly formatted. Correct statement is shown below:
Which equation has real zeros corresponding to the x-intercepts of the graph?
A. [tex]y = \log_{3} x - 1[/tex]
B. [tex]y = 3\cdot x -3[/tex]
C. [tex]y = -3\cdot (x-1) + 3[/tex]
D. [tex]y = \log_{3}2x -2[/tex]
To learn more on logarithms, we kindly invite to check this verified question: https://brainly.com/question/7302008
