Question

Compare the functions f(x)=x3+1 and g(x)=x+1.
Which of the following statements is true about the intercepts of the functions?

Answer 1

The intercepts of a function occur when the value of the function is 0.

For the function f(x) = x^3 + 1, to find the x-intercept, we set f(x) = 0 and solve for x:
x^3 + 1 = 0
x^3 = -1
x = -1

So, the x-intercept of f(x) is -1.

For the function g(x) = x + 1, to find the x-intercept, we set g(x) = 0 and solve for x:
x + 1 = 0
x = -1

So, the x-intercept of g(x) is also -1.

Therefore, the intercepts of both functions f(x) = x^3 + 1 and g(x) = x + 1 are the same, which is x = -1.

The statement "The intercepts of the functions are at the same x-value." is true.