Which of the following is the function for the graph below and shows the end behavior of the function as x ⟶ +∞?

f(x) = (4x^2 + 7x - 2)(2x + 3); f(x) ⟶ -∞
f(x) = (4x^2 - 7x - 2)(2x - 3); f(x) ⟶ +∞
f(x) = (4x^2 - 7x + 2)(2x - 3); f(x) ⟶ +∞
f(x) = (4x^2 - 7x - 2)(2x + 3); f(x) ⟶ -∞

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gmany gmany · Answer 1 · 2018-07-25T19:29:50+02:00

The simplest solution:

y - intercept of the function on the graph is (0; 6).

Only function f(x) = (4x^2 - 7x - 2)(2x - 3) has that y-intercept

f(0) = (4 · 0² - 7 · 0 - 2)(2 · 0 - 3) = (-2)(-3) = 6

Other functions have y - intercept equal (0; -6).

f(0) = (0 ... - 2)(0 + 3) = (-2)(3) = -6 or f(0) = (0 ... + 2)(0 - 3) = (2)(-3) = -6

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lisboa lisboa · Answer 2 · 2021-09-28T15:30:40+02:00

The function for the graph is [tex]f(x) = (4x^2 - 7x - 2)(2x - 3)[/tex] and shows the end behavior of the function as x ⟶ +∞, f(x) ⟶ +∞

Option B

Given :

The graph of a function . Lets analyze the end behavior of the given graph

When x approaches infinity on the right the graph goes up . It means the graph goes to + infinity

As x-> +∞, y -> +∞

So we look at the options B and C

Now, from the graph we can see that y intercept is (0,6)

Lets check options B and C that given y intercept (0,6)

Replace x with 0 and find out f(0)

[tex]f(x) = (4x^2 - 7x - 2)(2x - 3)\\x=0\\f(0) = (4(0)^2 - 7(0)- 2)(2(0)- 3)=6\\y intercept is (0,6)[/tex]

the function for the graph is [tex]f(x) = (4x^2 - 7x - 2)(2x - 3)[/tex] and shows the end behavior of the function as x ⟶ +∞, f(x) ⟶ +∞

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