Answer:
x-intercept → (-4, 0)
y-intercept → (0, -2.44)
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
Given function is f(x) = [tex]-\sqrt[3]{(x+3)}-1[/tex]
For x-intercept,
[tex]-\sqrt[3]{(x+3)}-1=0[/tex]
[tex]-\sqrt[3]{(x+3)}=1[/tex]
[tex]\sqrt[3]{(x+3)}=-1[/tex]
(x + 3) = -1
x = -4
Therefore, x-intercept → (-4, 0)
For y-intercept,
Substitute x = 0 in the function.
f(x) = [tex]-\sqrt[3]{(0+3)}-1[/tex]
= [tex]-\sqrt[3]{3}-1[/tex]
= -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: (-∞, ∞)
