Which function is graphed on the right? y=2x+3-2 y=2x-3+2 y=2x-2+3 y=2x-2-3
Accepted Solution
The equation of the function which is graphed on the right is specified by: Option C: y = 2^{x-2} + 3How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.A graph contains data of which input maps to which output.Analysis of this leads to the relations which were used to make it.For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.Since there is no graph available, we will work with the image attached below.The function, as visible is tending to output 3 and x goes more and more negative.That means:[tex]\lim_{x\rightarrow -\infty}f(x) = 3[/tex] (assuming the predicted pattern is true).Checking this for all the options:Case 1: [tex]y = f(x) = 2^{x+3} - 2[/tex][tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x+3} -2 = -2[/tex]
Thus, the graph doesn't belong to this function.Case 2: [tex]y = f(x) = 2^{x-3} + 2[/tex][tex]\lim_{x\rightarrow -\infty} f(x) = \lim_{x\rightarrow -\infty}2^{x-3} + 2 = 2[/tex]
Thus, the graph doesn't belong to this function.Case 3: [tex]y = f(x) = 2^{x-2} +3[/tex][tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} +3 = 3[/tex]
Thus, the graph may belong to this function. (we are still not sure since the last option may also have same limit, which if is found to be true, then additional findings would've to be done too).Case 4: [tex]y = f(x) = 2^{x-2} - 3[/tex][tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} -3 = -3[/tex]
Thus, the graph doesn't belong to this function.Thus, assuming at least one option is true, the graph of the considered function on the right is of the function [tex]y = f(x) = 2^{x-2} +3[/tex]Learn more about graphing functions here:
Thus, the graph doesn't belong to this function.Case 2: [tex]y = f(x) = 2^{x-3} + 2[/tex][tex]\lim_{x\rightarrow -\infty} f(x) = \lim_{x\rightarrow -\infty}2^{x-3} + 2 = 2[/tex]
Thus, the graph doesn't belong to this function.Case 3: [tex]y = f(x) = 2^{x-2} +3[/tex][tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} +3 = 3[/tex]
Thus, the graph may belong to this function. (we are still not sure since the last option may also have same limit, which if is found to be true, then additional findings would've to be done too).Case 4: [tex]y = f(x) = 2^{x-2} - 3[/tex][tex]\lim_{x\rightarrow -\infty}f(x) = \lim_{x\rightarrow -\infty} 2^{x-2} -3 = -3[/tex]
Thus, the graph doesn't belong to this function.Thus, assuming at least one option is true, the graph of the considered function on the right is of the function [tex]y = f(x) = 2^{x-2} +3[/tex]Learn more about graphing functions here: