Question

Select the correct answer.

The graph of function f is shown.

Function g is represented by the equation.
g(x) = 4(1/4)^x +2
Which statement correctly compares the two functions?

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

Answer 1

A. They have different y-intercepts but the same end behavior.

Explanation:

From the shape of f we see that its a descending exponential fnction, so the factor taken to the power x will be a fraction, and from the points the eqation is

f(x) = 2(1/4)^x + 2

and the y-intercept is 4

g(x) has y-intercept of 4(1/4)^0 + 2 = 6 so they are different.

As x approaches infinity both f and g approach 2 so the end behavior s the same.

Answer 2

A. They have different y-intercepts but the same end behavior.

Explanation:

You want to compare y-intercepts and end behavior of the function g(x) = 4(1/4)^x +2 and f(x) shown in the graph.

Y-intercepts

The y-intercept of each function is its value when x is zero.

f(0) = 4 . . . . from the graph

g(0) = 4(1/4)^0 +2 = 4 +2 = 6 . . . . . different y-intercept

End behavior

The end behavior of the function is the limiting value when x tends to infinity.

f(∞) ≈ 2 . . . . . . the horizontal asymptote is 2

g(∞) ≈ 2 . . . . . the horizontal asymptote is 2, same end behavior

The two functions have different y-intercepts and the same end behavior, choice A.

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