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End behaviour refers to the asymptotes, which both exponential functions have the same one at y = 2. However, they have different y - intercepts. The first one has a y - intercept of 4 and the second one has a y - intercept of 6. Thus, the answer is D.

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unicorn3125 unicorn3125 · Answer 2 · 2020-08-07T06:45:13+02:00

Answer:

D.

They have different y-intercepts but the same end behavior

Step-by-step explanation:

Let's name the function from graph: f

for f:

y-intercept = f(0) = 4

for x → ∞, f(x)→2

for g:

y-intercept = f(0) = 4(¹/₄)⁰+2 = 4•1+2 = 4+2 = 6 ≠4

f(1) = 4(¹/₄)¹+2 = 4•¹/₄+2 = 1+2 = 3

f(2) = 4(¹/₄)2+2 = 4•¹/₁₆+2 = ¹/₄+2 = 2¹/₄

f(3) = 4(¹/₄)³+2 = 4•¹/₆₄+2 = ¹/₁₆+2 = 2¹/₁₆

f((5) = 4(¹/₄)⁵+2 = 4•¹/₁₈₂₄+2 = ¹/₅₁₂+2 = 2¹/₅₁₂

....

so for x x → ∞, f(x)→2