Given:
[tex]g(x)=4(\frac{1}{4})^x+2[/tex]
Also the given graph is the graph of function f.
From the graph of function f, the y-intercept is at y = 4.
The y-intercept is the point the curve crosses the y-axis.
For function g(x), let's find the y-intercet.
To find the y-intercept, substitute 0 for x and solve for g(x).
[tex]\begin{gathered} g(0)=4(\frac{1}{4})^0+2 \\ \\ g(0)=4(1)+2 \\ \\ g(0)=6 \end{gathered}[/tex]
Therefore, the y-intercept of g(x) is at y = 6.
Hence, we have:
y-intercept of f(x): y = 4
y-intercept of g(x): y = 6
Both graphs have different y-intercepts.
Also, the graphs have the same end behaviours.
Therefore, the statement that correctly compares both functions is:
• T,hey have different y-intercepts but the same end behavior.
ANSWER:
A. They have different y-intercepts but the same end behavior.
