Question

A. They have different y-intercepts but the same end behavior. B. They have the same y-intercept and the same end behavior.C. They have the same y-intercept but different end behavior.D. They have different y-intercepts and different end behavior.Reset Next

Answer 1

Given:

`g(x)=4((1)/(4))^x+2`

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).

`\begin{gathered} g(0)=4((1)/(4))^0+2 \\ \\ g(0)=4(1)+2 \\ \\ g(0)=6 \end{gathered}`

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.