Question

Can anyone help me find the inflection point and how to solve this cubic function?

Answer 1

Answer:

x-intercept → (-4, 0)

y-intercept → (0, -2.44)

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

Given function is f(x) = $-\sqrt[3]{(x+3)}-1$

For x-intercept,

$-\sqrt[3]{(x+3)}-1=0$

$-\sqrt[3]{(x+3)}=1$

$\sqrt[3]{(x+3)}=-1$

(x + 3) = -1

x = -4

Therefore, x-intercept → (-4, 0)

For y-intercept,

Substitute x = 0 in the function.

f(x) = $-\sqrt[3]{(0+3)}-1$

     = $-\sqrt[3]{3}-1$

     = -1.44 - 1

     = -2.44

Therefore, y-intercept → (0, -2.44)

Domain: This function is defined for all real values of x.

Therefore, Domain: (-∞, ∞)

Range: Since this function is defined for all real values of x, we will get a distinct output value for every distinct input values.

Therefore, Range: (-∞, ∞)