Compare the functions f (x)= x^3 +1 and g(x)=x + 1. Which of the following statements is true about the intercepts of the functions?
• Both functions have an x-intercept of (-1, 0) and a y-intercept of (0, 1).
• The x- and y-intercepts are different for each function.
• The graphs intersect at (1, 2).
• Both functions have a y-intercept of (-1, 0) and an x-intercept of (0, 1).
The correct statement is: The x- and y-intercepts are different for each function.
For the function f(x)= x^3 +1, in order to find the x-intercept, we set y = 0 and solve for x:
0 = x^3 + 1
-1 = x^3
x = -1
So, f(x) has an x-intercept at (-1, 0).
To find the y-intercept, we set x = 0 and solve for y:
y = 0^3 + 1
y = 1
So, f(x) has a y-intercept at (0, 1).
For the function g(x) = x + 1, in order to find the x-intercept, we set y = 0 and solve for x:
0 = x + 1
x = -1
So, g(x) has an x-intercept at (-1, 0).
To find the y-intercept, we set x = 0 and solve for y:
y = 0 + 1
y = 1
So, g(x) has a y-intercept at (0, 1).
Therefore, the x- and y-intercepts are different for each function.